New Research On Cancer's Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV

Henry Garrett

doi:10.13140/RG.2.2.34946.96960

Published February 6, 2023 | Version v1

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New Research On Cancer's Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV

Henry Garrett¹

1. Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA

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Research – February 05, 2023
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\fancyhead[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA }
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\textbf\newline{
New Research On Cancer's Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV
}
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Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA
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\section*{ABSTRACT}
In this research, assume a SuperHyperGraph. Then some notions on Extreme SuperHyperCycle based on the backgrounds of Eulerian and Hamiltonian styles are proposed. Some results are directed in the way that, the starting definitions make sense on the motivation and the continuous approaches for this research. A basic familiarity with neutrosophic SuperHyperCycle theory, SuperHyperGraphs, and neutrosophic SuperHyperGraphs theory are proposed.
\\ \vspace{4mm}
\textbf{Keywords:} neutrosophic SuperHyperGraph, (neutrosophic) SuperHyperCycle, Cancer's neutrosophic Recognition
\\
\textbf{AMS Subject Classification:} 05C17, 05C22, 05E45
\section{Wondering open Problems But As The Directions To Forming The Motivations}
In what follows, some ``Neutrosophic problems'' and some ``Neutrosophic questions'' are Neutrosophicly proposed.
\\
The SuperHyperCycle and the neutrosophic SuperHyperCycle are Neutrosophicly defined on a real-world Neutrosophic application, titled ``Cancer's neutrosophic recognitions''.
\begin{question}
Which the else neutrosophic SuperHyperModels could be defined based on Cancer's neutrosophic recognitions?
\end{question}
\begin{question}
Are there some neutrosophic SuperHyperNotions related to SuperHyperCycle and the neutrosophic SuperHyperCycle?
\end{question}
\begin{question}
Are there some Neutrosophic Algorithms to be defined on the neutrosophic SuperHyperModels to compute them Neutrosophicly?
\end{question}
\begin{question}
Which the neutrosophic SuperHyperNotions are related to beyond the SuperHyperCycle and the neutrosophic SuperHyperCycle?
\end{question}
\begin{problem}
The SuperHyperCycle and the neutrosophic SuperHyperCycle do Neutrosophicly a neutrosophic SuperHyperModel for the Cancer's neutrosophic recognitions and they're based Neutrosophicly on neutrosophic SuperHyperCycle, are there else Neutrosophicly?
\end{problem}
\begin{problem}
Which the fundamental Neutrosophic SuperHyperNumbers are related to these Neutrosophic SuperHyperNumbers types-results?
\end{problem}
\begin{problem}
What's the independent research based on Cancer's neutrosophic recognitions concerning the multiple types of neutrosophic SuperHyperNotions?
\end{problem}

\section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation}

\begin{proposition}
Let $ESHG:(V,E)$ be an odd SuperHyperPath. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is a dual SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$]
$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$;
\item[$(iii)$]
$\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$
\item[$(iv)$]
the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only a dual SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
Let $ESHG:(V,E)$ be an even SuperHyperPath. Then
\begin{itemize}
\item[$(i)$]
the set $S=\{v_2,v_4,\cdots.v_{n}\}$ is a dual SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$]
$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots.v_n\}$ and $\{v_1,v_3,\cdots.v_{n-1}\};$
\item[$(iii)$]
$\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$
\item[$(iv)$]
the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
Let $ESHG:(V,E)$ be an even SuperHyperCycle. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n}\}$ is a dual SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$]
$\Gamma=\lfloor\frac{n}{2}\rfloor$ and corresponded SuperHyperSets are $\{v_2,v_4,\cdots,v_n\}$ and $\{v_1,v_3,\cdots,v_{n-1}\};$
\item[$(iii)$]
$\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots,v_n\}}\sigma(s), \Sigma_{s\in S=\{v_1,v_3,\cdots,v_{n-1}\}}\sigma(s)\};$
\item[$(iv)$]
the SuperHyperSets $S_1=\{v_2,v_4,\cdots,v_{n}\}$ and $S_2=\{v_1,v_3,\cdots,v_{n-1}\}$ are only dual SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
Let $ESHG:(V,E)$ be an odd SuperHyperCycle. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{v_2,v_4,\cdots,v_{n-1}\}$ is a dual SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$]
$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ and corresponded SuperHyperSet is $S=\{v_2,v_4,\cdots,v_{n-1}\}$;
\item[$(iii)$]
$\Gamma_s=\min\{\Sigma_{s\in S=\{v_2,v_4,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s), \Sigma_{s\in S=\{v_1,v_3,\cdots.v_{n-1}\}}\Sigma_{i=1}^3\sigma_i(s)\};$
\item[$(iv)$]
the SuperHyperSets $S_1=\{v_2,v_4,\cdots.v_{n-1}\}$ and $S_2=\{v_1,v_3,\cdots.v_{n-1}\}$ are only dual SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
Let $ESHG:(V,E)$ be SuperHyperStar. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{c\}$ is a dual maximal SuperHyperCycle;
\item[$(ii)$]
$\Gamma=1;$
\item[$(iii)$]
$\Gamma_s=\Sigma_{i=1}^3\sigma_i(c);$
\item[$(iv)$]
the SuperHyperSets $S=\{c\}$ and $S\subset S'$ are only dual SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
Let $ESHG:(V,E)$ be SuperHyperWheel. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is a dual maximal SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$]
$\Gamma=|\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}|;$
\item[$(iii)$]
$\Gamma_s=\Sigma_{\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}}\Sigma_{i=1}^3\sigma_i(s);$
\item[$(iv)$]
the SuperHyperSet $\{v_1,v_3\}\cup\{v_6,v_9\cdots,v_{i+6},\cdots,v_n\}_{i=1}^{6+3(i-1)\leq n}$ is only a dual maximal SuperHyperDefensive SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
Let $ESHG:(V,E)$ be an odd SuperHyperComplete. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is a dual SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$]
$\Gamma=\lfloor\frac{n}{2}\rfloor+1;$
\item[$(iii)$]
$\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}};$
\item[$(iv)$]
the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is only a dual SuperHyperDefensive SuperHyperCycle.
\end{itemize}
\end{proposition}

\begin{proposition}
Let $ESHG:(V,E)$ be an even SuperHyperComplete. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$]
$\Gamma=\lfloor\frac{n}{2}\rfloor;$
\item[$(iii)$]
$\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}};$
\item[$(iv)$]
the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is only a dual maximal SuperHyperDefensive SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of neutrosophic SuperHyperStars with common neutrosophic SuperHyperVertex SuperHyperSet. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{c_1,c_2,\cdots,c_m\}$ is a dual SuperHyperDefensive SuperHyperCycle for $\mathcal{NSHF};$
\item[$(ii)$]
$\Gamma=m$ for $\mathcal{NSHF}:(V,E);$
\item[$(iii)$]
$\Gamma_s=\Sigma_{i=1}^m\Sigma_{j=1}^3\sigma_j(c_i)$ for $\mathcal{NSHF}:(V,E);$
\item[$(iv)$]
the SuperHyperSets $S=\{c_1,c_2,\cdots,c_m\}$ and $S\subset S'$ are only dual SuperHyperCycle for $\mathcal{NSHF}:(V,E).$
\end{itemize}
\end{proposition}
\begin{proposition}
Let $\mathcal{NSHF}:(V,E)$ be an $m$-SuperHyperFamily of odd SuperHyperComplete SuperHyperGraphs with common neutrosophic SuperHyperVertex SuperHyperSet. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ is a dual maximal SuperHyperDefensive SuperHyperCycle for $\mathcal{NSHF};$
\item[$(ii)$]
$\Gamma=\lfloor\frac{n}{2}\rfloor+1$ for $\mathcal{NSHF}:(V,E);$
\item[$(iii)$]
$\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}}$ for $\mathcal{NSHF}:(V,E);$
\item[$(iv)$]
the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor+1}$ are only a dual maximal SuperHyperCycle for $\mathcal{NSHF}:(V,E).$
\end{itemize}
\end{proposition}
\begin{proposition}
Let $\mathcal{NSHF}:(V,E)$ be a $m$-SuperHyperFamily of even SuperHyperComplete SuperHyperGraphs with common neutrosophic SuperHyperVertex SuperHyperSet. Then
\begin{itemize}
\item[$(i)$]
the SuperHyperSet $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ is a dual SuperHyperDefensive SuperHyperCycle for $\mathcal{NSHF}:(V,E);$
\item[$(ii)$]
$\Gamma=\lfloor\frac{n}{2}\rfloor$ for $\mathcal{NSHF}:(V,E);$
\item[$(iii)$]
$\Gamma_s=\min\{\Sigma_{s\in S}\Sigma_{i=1}^3\sigma_i(s)\}_{S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}}$ for $\mathcal{NSHF}:(V,E);$
\item[$(iv)$]
the SuperHyperSets $S=\{v_i\}_{i=1}^{\lfloor\frac{n}{2}\rfloor}$ are only dual maximal SuperHyperCycle for $\mathcal{NSHF}:(V,E).$
\end{itemize}
\end{proposition}
\begin{proposition}
   Let $ESHG:(V,E)$ be a[an] [r-]SuperHyperUniform-strong-neutrosophic SuperHyperGraph. Then following statements hold;
\begin{itemize}
\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|< \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$] if $\forall a\in V\setminus S,~|N_s(a)\cap S|> \lfloor \frac{r}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperCycle;
   \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an r-SuperHyperDefensive SuperHyperCycle;
     \item[$(iv)$] if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual r-SuperHyperDefensive SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
   Let $ESHG:(V,E)$ is a[an] [r-]SuperHyperUniform-strong-neutrosophic SuperHyperGraph. Then following statements hold;
\begin{itemize}
\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|< \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$] $\forall a\in V\setminus S,~|N_s(a)\cap S|> \lfloor \frac{r}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperCycle;
   \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an r-SuperHyperDefensive SuperHyperCycle;
     \item[$(iv)$] $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual r-SuperHyperDefensive SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
   Let $ESHG:(V,E)$ is a[an] [r-]SuperHyperUniform-strong-neutrosophic SuperHyperGraph which is a SuperHyperComplete. Then following statements hold;
\begin{itemize}
\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|< \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$] $\forall a\in V\setminus S,~|N_s(a)\cap S|> \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperCycle;
   \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an $(\mathcal{O}-1)$-SuperHyperDefensive SuperHyperCycle;
     \item[$(iv)$] $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
   Let $ESHG:(V,E)$ is a[an] [r-]SuperHyperUniform-strong-neutrosophic SuperHyperGraph which is a SuperHyperComplete. Then following statements hold;
\begin{itemize}
\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|< \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$] if $\forall a\in V\setminus S,~|N_s(a)\cap S|> \lfloor \frac{\mathcal{O}-1}{2}\rfloor+1,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperCycle;
   \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is $(\mathcal{O}-1)$-SuperHyperDefensive SuperHyperCycle;
     \item[$(iv)$] if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual $(\mathcal{O}-1)$-SuperHyperDefensive SuperHyperCycle.
\end{itemize}
\end{proposition}
\begin{proposition}
   Let $ESHG:(V,E)$ is a[an] [r-]SuperHyperUniform-strong-neutrosophic SuperHyperGraph which is SuperHyperCycle. Then following statements hold;
\begin{itemize}
\item[$(i)$] $\forall a\in S,~|N_s(a)\cap S|< 2$ if $ESHG:(V,E))$ is an 2-SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$] $\forall a\in V\setminus S,~|N_s(a)\cap S|> 2$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperCycle;
   \item[$(iii)$] $\forall a\in S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperCycle;
     \item[$(iv)$] $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0$ if $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperCycle.
\end{itemize}
\end{proposition}

\begin{proposition}
   Let $ESHG:(V,E)$ is a[an] [r-]SuperHyperUniform-strong-neutrosophic SuperHyperGraph which is SuperHyperCycle. Then following statements hold;
\begin{itemize}
\item[$(i)$] if $\forall a\in S,~|N_s(a)\cap S|< 2,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperCycle;
\item[$(ii)$] if $\forall a\in V\setminus S,~|N_s(a)\cap S|> 2,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperCycle;
   \item[$(iii)$] if $\forall a\in S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is an 2-SuperHyperDefensive SuperHyperCycle;
     \item[$(iv)$] if $\forall a\in V\setminus S,~|N_s(a)\cap V\setminus S|=0,$ then $ESHG:(V,E)$ is a dual 2-SuperHyperDefensive SuperHyperCycle.
\end{itemize}
\end{proposition}

\section{Applied Notions Under The Scrutiny Of The Motivation Of This Research}
In this research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways.
\begin{question}
How to define the SuperHyperNotions and to do research on them to find the `` amount of SuperHyperCycle'' of either individual of cells or the groups of cells based on the fixed cell or the fixed group of cells, extensively, the ``amount of SuperHyperCycle'' based on the fixed groups of cells or the fixed groups of group of cells?
\end{question}
\begin{question}
What are the best descriptions for the ``Cancer's Recognition'' in terms of these messy and dense SuperHyperModels where embedded notions are illustrated?
\end{question}
It's motivation to find notions to use in this dense model is titled ``SuperHyperGraphs''. Thus it motivates us to define different types of `` SuperHyperCycle'' and ``neutrosophic SuperHyperCycle'' on ``SuperHyperGraph'' and ``neutrosophic SuperHyperGraph''. \section{Preliminaries Of This Research On the Redeemed Ways}
\section{Preliminaries}
In this section, the basic material in this research, is referred to [Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2), [Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1), [Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2), [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3), and [Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3), [Neutrosophic Strength of the Neutrosophic SuperHyperPaths] (\textbf{Ref.}\cite{HG38},Definition 5.3,p.7), and [Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)] (\textbf{Ref.}\cite{HG38},Definition 5.4,p.7). Also, the new ideas and their clarifications are addressed to \textbf{Ref.}\cite{HG38}.
\\
In this subsection, the basic material which is used in this research, is presented. Also, the new ideas and their clarifications are elicited.
\begin{definition}[Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.1,p.1).\\
Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x;$ then the \textbf{Neutrosophic set} $A$ (NS $A$) is an object having the form
$$A = \{< x:T_A(x),I_A(x),F_A(x)>, x\in X\}$$
where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition
$$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$
The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$
\end{definition}
\begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{HG38},Definition 2.2,p.2).\\
Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued Neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as
$$A = \{< x:T_A(x),I_A(x),F_A(x)>, x\in X\}.$$
\end{definition}
\begin{definition}
The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set $A = \{< x:T_A(x),I_A(x),F_A(x)>, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$
$$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$
$$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$
\end{definition}
\begin{definition}
The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set $A = \{< x:T_A(x),I_A(x),F_A(x)>, x\in X\}$:
$$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)> 0\}.$$
\end{definition}
\begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.5,p.2).\\
Assume $V'$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$
is an ordered pair $S=(V,E),$ where
\begin{itemize}
\item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V';$
\item[$(ii)$] $V=\{(V_i,T_{V'}(V_i),I_{V'}(V_i),F_{V'}(V_i)):~T_{V'}(V_i),I_{V'}(V_i),F_{V'}(V_i)\geq0\},~(i=1,2,\ldots,n);$
\item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n'}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$
\item[$(iv)$] $E=\{(E_{i'},T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'})):~T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'})\geq0\},~(i'=1,2,\ldots,n');$
\item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$
\item[$(vi)$] $E_{i'}\neq\emptyset,~(i'=1,2,\ldots,n');$
\item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$
\item[$(viii)$] $\sum_{i'}supp(E_{i'})=V,~(i'=1,2,\ldots,n');$
\item[$(ix)$] and the following conditions hold:
$$T'_V(E_{i'})\leq\min[T_{V'}(V_i),T_{V'}(V_j)]_{V_i,V_j\in E_{i'}},$$
$$ I'_V(E_{i'})\leq\min[I_{V'}(V_i),I_{V'}(V_j)]_{V_i,V_j\in E_{i'}},$$
$$ \text{and}~F'_V(E_{i'})\leq\min[F_{V'}(V_i),F_{V'}(V_j)]_{V_i,V_j\in E_{i'}}$$
where $i'=1,2,\ldots,n'.$
\end{itemize}
Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j'}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V'}(V_i),I_{V'}(V_i),$ and $F_{V'}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T'_{V}(E_{i'}),T'_{V}(E_{i'}),$ and $T'_{V}(E_{i'})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i'}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii'$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'}))$, the sets V and E are crisp sets.
\end{definition}
\begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\
Assume a Neutrosophic SuperHyperGraph (NSHG) $S$
is an ordered pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i'}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items.
\begin{itemize}
\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex};
\item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex};
\item[$(iii)$] if for all $V_i$s are incident in $E_{i'},$ $|V_i|=1,$ and $|E_{i'}|=2,$ then $E_{i'}$ is called \textbf{edge};
\item[$(iv)$] if for all $V_i$s are incident in $E_{i'},$ $|V_i|=1,$ and $|E_{i'}|\geq2,$ then $E_{i'}$ is called \textbf{HyperEdge};
\item[$(v)$] if there's a $V_i$ is incident in $E_{i'}$ such that $|V_i|\geq1,$ and $|E_{i'}|=2,$ then $E_{i'}$ is called \textbf{SuperEdge};
\item[$(vi)$] if there's a $V_i$ is incident in $E_{i'}$ such that $|V_i|\geq1,$ and $|E_{i'}|\geq2,$ then $E_{i'}$ is called \textbf{SuperHyperEdge}.
\end{itemize}
\end{definition}
If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG).
\begin{definition}[t-norm](\textbf{Ref.}\cite{HG38}, Definition 2.7, p.3).\\
A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w \in [0, 1]$:
\begin{itemize}
\item[$(i)$] $1 \otimes x =x;$
\item[$(ii)$] $x \otimes y = y \otimes x;$
\item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$
\item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$
\end{itemize}
\end{definition}
\begin{definition}
The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued Neutrosophic set $A = \{< x:T_A(x),I_A(x),F_A(x)>, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$
$$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$
$$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$
\end{definition}
\begin{definition}
The \textbf{support} of $X\subset A$ of the single valued Neutrosophic set $A = \{< x:T_A(x),I_A(x),F_A(x)>, x\in X\}$:
$$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)> 0\}.$$
\end{definition}
\begin{definition}(General Forms of Neutrosophic SuperHyperGraph (NSHG)).\\
Assume $V'$ is a given set. a \textbf{Neutrosophic SuperHyperGraph} (NSHG) $S$
is an ordered pair $S=(V,E),$ where
\begin{itemize}
\item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued Neutrosophic subsets of $V';$
\item[$(ii)$] $V=\{(V_i,T_{V'}(V_i),I_{V'}(V_i),F_{V'}(V_i)):~T_{V'}(V_i),I_{V'}(V_i),F_{V'}(V_i)\geq0\},~(i=1,2,\ldots,n);$
\item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n'}\}$ a finite set of finite single valued Neutrosophic subsets of $V;$
\item[$(iv)$] $E=\{(E_{i'},T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'})):~T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'})\geq0\},~(i'=1,2,\ldots,n');$
\item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$
\item[$(vi)$] $E_{i'}\neq\emptyset,~(i'=1,2,\ldots,n');$
\item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$
\item[$(viii)$] $\sum_{i'}supp(E_{i'})=V,~(i'=1,2,\ldots,n').$
\end{itemize}
Here the Neutrosophic SuperHyperEdges (NSHE) $E_{j'}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued Neutrosophic sets. $T_{V'}(V_i),I_{V'}(V_i),$ and $F_{V'}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the Neutrosophic SuperHyperVertex (NSHV) $V_i$ to the Neutrosophic SuperHyperVertex (NSHV) $V.$ $T'_{V}(E_{i'}),T'_{V}(E_{i'}),$ and $T'_{V}(E_{i'})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the Neutrosophic SuperHyperEdge (NSHE) $E_{i'}$ to the Neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii'$th element of the \textbf{incidence matrix} of Neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'}))$, the sets V and E are crisp sets.
\end{definition}

\begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{HG38},Definition 2.7,p.3).\\
Assume a Neutrosophic SuperHyperGraph (NSHG) $S$
is an ordered pair $S=(V,E).$ The Neutrosophic SuperHyperEdges (NSHE) $E_{i'}$ and the Neutrosophic SuperHyperVertices (NSHV) $V_i$ of Neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items.
\begin{itemize}
\item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex};
\item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex};
\item[$(iii)$] if for all $V_i$s are incident in $E_{i'},$ $|V_i|=1,$ and $|E_{i'}|=2,$ then $E_{i'}$ is called \textbf{edge};
\item[$(iv)$] if for all $V_i$s are incident in $E_{i'},$ $|V_i|=1,$ and $|E_{i'}|\geq2,$ then $E_{i'}$ is called \textbf{HyperEdge};
\item[$(v)$] if there's a $V_i$ is incident in $E_{i'}$ such that $|V_i|\geq1,$ and $|E_{i'}|=2,$ then $E_{i'}$ is called \textbf{SuperEdge};
\item[$(vi)$] if there's a $V_i$ is incident in $E_{i'}$ such that $|V_i|\geq1,$ and $|E_{i'}|\geq2,$ then $E_{i'}$ is called \textbf{SuperHyperEdge}.
\end{itemize}
\end{definition}
This SuperHyperModel is too messy and too dense. Thus there's a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities.
\begin{definition}
A graph is \textbf{SuperHyperUniform} if it's SuperHyperGraph and the number of elements of SuperHyperEdges are the same.
\end{definition}
To get more visions on SuperHyperUniform, the some SuperHyperClasses are introduced. It makes to have SuperHyperUniform more understandable.
\begin{definition}
Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows.
\begin{itemize}
\item[(i).] It's \textbf{Neutrosophic SuperHyperPath } if it's only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions;
\item[(ii).] it's \textbf{SuperHyperCycle} if it's only one SuperVertex as intersection amid two given SuperHyperEdges;
\item[(iii).] it's \textbf{SuperHyperStar} it's only one SuperVertex as intersection amid all SuperHyperEdges;
   \item[(iv).] it's \textbf{SuperHyperBipartite} it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common;
    \item[(v).] it's \textbf{SuperHyperMultiPartite} it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common;
     \item[(vi).] it's \textbf{SuperHyperWheel} if it's only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex.

\end{itemize}
\end{definition}

\begin{definition}
Let an ordered pair $S=(V,E)$ be a Neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE)
$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$
is called a \textbf{Neutrosophic Neutrosophic SuperHyperPath } (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold:
\begin{itemize}
\item[$(i)$] $V_i,V_{i+1}\in E_{i'};$
\item[$(ii)$]   there's a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i'};$
\item[$(iii)$] there's a SuperVertex $V'_i \in V_i$ such that $V'_i,V_{i+1}\in E_{i'};$
   \item[$(iv)$]   there's a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i'};$
\item[$(v)$] there's a SuperVertex $V'_{i+1} \in V_{i+1}$ such that $V_i,V'_{i+1}\in E_{i'};$
   \item[$(vi)$]   there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i'};$
\item[$(vii)$]   there are a vertex $v_i\in V_i$ and a SuperVertex $V'_{i+1} \in V_{i+1}$ such that $v_i,V'_{i+1}\in E_{i'};$
     \item[$(viii)$]   there are a SuperVertex $V'_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V'_i,v_{i+1}\in E_{i'};$
\item[$(ix)$]   there are a SuperVertex $V'_i\in V_i$ and a SuperVertex $V'_{i+1} \in V_{i+1}$ such that $V'_i,V'_{i+1}\in E_{i'}.$
\end{itemize}
\end{definition}

\begin{definition}(Characterization of the Neutrosophic Neutrosophic SuperHyperPaths).\\
Assume a Neutrosophic SuperHyperGraph (NSHG) $S$
is an ordered pair $S=(V,E).$ a Neutrosophic Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE)
$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$
could be characterized as follow-up items.
\begin{itemize}
\item[$(i)$] If for all $V_i,E_{j'},$ $|V_i|=1,~|E_{j'}|=2,$ then NSHP is called \textbf{path};
\item[$(ii)$] if for all $E_{j'},$ $|E_{j'}|=2,$ and there's $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath};
\item[$(iii)$] if for all $V_i,E_{j'},$ $|V_i|=1,~|E_{j'}|\geq2,$ then NSHP is called \textbf{HyperPath};
\item[$(iv)$] if there are $V_i,E_{j'},$ $|V_i|\geq1,|E_{j'}|\geq2,$ then NSHP is called \textbf{Neutrosophic SuperHyperPath }.
\end{itemize}
\end{definition}
\begin{definition}[Neutrosophic Strength of the Neutrosophic SuperHyperPaths](\textbf{Ref.}\cite{HG38},Definition 5.3,p.7).\\
Assume a Neutrosophic SuperHyperGraph (NSHG) $S$
is an ordered pair $S=(V,E).$ A Neutrosophic SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_1$ to Neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of Neutrosophic SuperHyperVertices (NSHV) and Neutrosophic SuperHyperEdges (NSHE)
$$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$
have
\begin{itemize}
\item[$(i)$]\textbf{Neutrosophic t-strength} $(\min\{T(V_i)\},m,n)_{i=1}^s$;
\item[$(ii)$] \textbf{Neutrosophic i-strength} $(m,\min\{I(V_i)\},n)_{i=1}^s;$
\item[$(iii)$] \textbf{Neutrosophic f-strength} $(m,n,\min\{F(V_i)\})_{i=1}^s;$
\item[$(iv)$] \textbf{Neutrosophic strength} $(\min\{T(V_i)\},\min\{I(V_i)\},\min\{F(V_i)\})_{i=1}^s.$
\end{itemize}
\end{definition}

\begin{definition}[Different Neutrosophic Types of Neutrosophic SuperHyperEdges (NSHE)](\textbf{Ref.}\cite{HG38},Definition 5.4,p.7).\\
Assume a Neutrosophic SuperHyperGraph (NSHG) $S$
is an ordered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\ldots,V_s\}.$
Then $E$ is called
\begin{itemize}
\item[$(ix)$] \textbf{Neutrosophic t-connective} if $T(E)\geq$ maximum number of Neutrosophic t-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$
\item[$(x)$] \textbf{Neutrosophic i-connective} if $I(E)\geq$ maximum number of Neutrosophic i-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$
\item[$(xi)$] \textbf{Neutrosophic f-connective} if $F(E)\geq$ maximum number of Neutrosophic f-strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s;$
\item[$(xii)$] \textbf{Neutrosophic connective} if $(T(E),I(E),F(E))\geq$ maximum number of Neutrosophic strength of SuperHyperPath (NSHP) from Neutrosophic SuperHyperVertex (NSHV) $V_i$ to Neutrosophic SuperHyperVertex (NSHV) $V_j$ where $1\leq i,j\leq s.$
\end{itemize}
\end{definition}

\begin{definition}((neutrosophic) SuperHyperCycle).\\
Assume a SuperHyperGraph. Then
\begin{itemize}
\item[$(i)$]
an \textbf{Extreme SuperHyperCycle} $\mathcal{C}(NSHG)$ for an extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum extreme cardinality of an extreme SuperHyperSet $S$ of high extreme cardinality of the extreme SuperHyperEdges in the consecutive extreme sequence of extreme SuperHyperEdges and extreme SuperHyperVertices such that they form the extreme SuperHyperCycle and either all extreme SuperHyperVertices or all extreme SuperHyperEdges;
\item[$(ii)$]
a \textbf{Neutrosophic SuperHyperCycle} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of the neutrosophic SuperHyperEdges of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality consecutive neutrosophic SuperHyperEdges and neutrosophic SuperHyperVertices such that they form the neutrosophic SuperHyperCycle and either all neutrosophic SuperHyperVertices or all neutrosophic SuperHyperEdges;
\item[$(iii)$]
an \textbf{Extreme SuperHyperCycle SuperHyperPolynomial} $\mathcal{C}(NSHG)$ for an extreme SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the extreme coefficients defined as the extreme number of the maximum extreme cardinality of the extreme SuperHyperEdges of an extreme SuperHyperSet $S$ of high extreme cardinality consecutive extreme SuperHyperEdges and extreme SuperHyperVertices such that they form the extreme SuperHyperCycle and either all extreme SuperHyperVertices or all extreme SuperHyperEdges; and the extreme power is corresponded to its extreme coefficient;
\item[$(iv)$]
a \textbf{Neutrosophic SuperHyperCycle SuperHyperPolynomial} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of the neutrosophic SuperHyperEdges of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality consecutive neutrosophic SuperHyperEdges and neutrosophic SuperHyperVertices such that they form the neutrosophic SuperHyperCycle and either all neutrosophic SuperHyperVertices or all neutrosophic SuperHyperEdges; and the neutrosophic power is corresponded to its neutrosophic coefficient;
\item[$(v)$]
an \textbf{Extreme R-SuperHyperCycle} $\mathcal{C}(NSHG)$ for an extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum extreme cardinality of an extreme SuperHyperSet $S$ of high extreme cardinality of the extreme SuperHyperVertices in the consecutive extreme sequence of extreme SuperHyperEdges and extreme SuperHyperVertices such that they form the extreme SuperHyperCycle and either all extreme SuperHyperVertices or all extreme SuperHyperEdges;
\item[$(vi)$]
a \textbf{Neutrosophic R-SuperHyperCycle} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of the neutrosophic SuperHyperVertices of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality consecutive neutrosophic SuperHyperEdges and neutrosophic SuperHyperVertices such that they form the neutrosophic SuperHyperCycle and either all neutrosophic SuperHyperVertices or all neutrosophic SuperHyperEdges;;
\item[$(vii)$]
an \textbf{Extreme R-SuperHyperCycle SuperHyperPolynomial} $\mathcal{C}(NSHG)$ for an extreme SuperHyperGraph $NSHG:(V,E)$ is the extreme SuperHyperPolynomial contains the extreme coefficients defined as the extreme number of the maximum extreme cardinality of the extreme SuperHyperVertices of an extreme SuperHyperSet $S$ of high extreme cardinality consecutive extreme SuperHyperEdges and extreme SuperHyperVertices such that they form the extreme SuperHyperCycle and either all extreme SuperHyperVertices or all extreme SuperHyperEdges; and the extreme power is corresponded to its extreme coefficient;
\item[$(viii)$]
a \textbf{Neutrosophic SuperHyperCycle SuperHyperPolynomial} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of the neutrosophic SuperHyperVertices of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality consecutive neutrosophic SuperHyperEdges and neutrosophic SuperHyperVertices such that they form the neutrosophic SuperHyperCycle and either all neutrosophic SuperHyperVertices or all neutrosophic SuperHyperEdges; and the neutrosophic power is corresponded to its neutrosophic coefficient.
\end{itemize}
\end{definition}
\begin{definition}((neutrosophic/neutrosophic)$\delta-$SuperHyperCycle).\\
Assume a SuperHyperGraph. Then
\begin{itemize}
\item[$(i)$] an \textbf{$\delta-$SuperHyperCycle} is a neutrosophic kind of neutrosophic SuperHyperCycle such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$
\begin{eqnarray*}
&&|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta; \label{134EQN1}
\\&& |S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta. \label{134EQN2}
\end{eqnarray*}
The Expression \eqref{134EQN1}, holds if $S$ is an \textbf{$\delta-$SuperHyperOffensive}. And the Expression \eqref{134EQN2}, holds if $S$ is an \textbf{$\delta-$SuperHyperDefensive};
\item[$(ii)$] a \textbf{Neutrosophic $\delta-$SuperHyperCycle} is a neutrosophic kind of neutrosophic SuperHyperCycle such that either of the following neutrosophic expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$
\begin{eqnarray*}
&&|S\cap N(s)|_{Neutrosophic} > |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta; \label{134EQN3}
\\&& |S\cap N(s)|_{Neutrosophic} < |S\cap (V\setminus N(s))|_{Neutrosophic}+\delta. \label{134EQN4}
\end{eqnarray*}
The Expression \eqref{134EQN3}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{134EQN4}, holds if $S$ is a \textbf{Neutrosophic $\delta-$SuperHyperDefensive}.
\end{itemize}
\end{definition}
For the sake of having a neutrosophic SuperHyperCycle, there's a need to ``\textbf{redefine}'' the notion of ``neutrosophic SuperHyperGraph''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values.
\begin{definition}\label{134DEF1}
Assume a neutrosophic SuperHyperGraph. It's redefined \textbf{Neutrosophic SuperHyperGraph} if the Table \eqref{134TBL3} holds.
\begin{table}
\centering
\caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{134DEF1}}
\begin{tabular}[t]{c|c}
\hline
The Values of The Vertices & The Number of Position in Alphabet\\
\hline
The Values of The SuperVertices&The maximum Values of Its Vertices\\
\hline
The Values of The Edges&The maximum Values of Its Vertices\\
\hline
The Values of The HyperEdges&The maximum Values of Its Vertices\\
\hline
The Values of The SuperHyperEdges&The maximum Values of Its Endpoints \\
\hline
\end{tabular}
\label{134TBL3}
\end{table}
\end{definition}
It's useful to define a ``neutrosophic'' version of SuperHyperClasses. Since there's more ways to get neutrosophic type-results to make a neutrosophic more understandable.
\begin{definition}\label{134DEF2}
Assume a neutrosophic SuperHyperGraph. There are some \textbf{Neutrosophic SuperHyperClasses} if the Table \eqref{134TBL4} holds. Thus neutrosophic SuperHyperPath , SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are
\textbf{Neutrosophic SuperHyperPath }, \textbf{Neutrosophic SuperHyperCycle}, \textbf{Neutrosophic SuperHyperStar}, \textbf{Neutrosophic SuperHyperBipartite}, \textbf{Neutrosophic SuperHyperMultiPartite}, and \textbf{Neutrosophic SuperHyperWheel} if the Table \eqref{134TBL4} holds.
\begin{table}
\centering
\caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{134DEF2}}
\begin{tabular}[t]{c|c}
\hline
The Values of The Vertices & The Number of Position in Alphabet\\
\hline
The Values of The SuperVertices&The maximum Values of Its Vertices\\
\hline
The Values of The Edges&The maximum Values of Its Vertices\\
\hline
The Values of The HyperEdges&The maximum Values of Its Vertices\\
\hline
The Values of The SuperHyperEdges&The maximum Values of Its Endpoints \\
\hline
\end{tabular}
\label{134TBL4}
\end{table}
\end{definition}
It's useful to define a ``neutrosophic'' version of a neutrosophic SuperHyperCycle. Since there's more ways to get type-results to make a neutrosophic SuperHyperCycle more neutrosophicly understandable.
\\
For the sake of having a neutrosophic SuperHyperCycle, there's a need to ``\textbf{redefine}'' the neutrosophic notion of ``neutrosophic SuperHyperCycle''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values.
\begin{definition}\label{134DEF1}
Assume a SuperHyperCycle. It's redefined a \textbf{Neutrosophic SuperHyperCycle} if the Table \eqref{134TBL1} holds. \begin{table}
\centering
\caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{134DEF1}}
\begin{tabular}[t]{c|c}
\hline
The Values of The Vertices & The Number of Position in Alphabet\\
\hline
The Values of The SuperVertices&The maximum Values of Its Vertices\\
\hline
The Values of The Edges&The maximum Values of Its Vertices\\
\hline
The Values of The HyperEdges&The maximum Values of Its Vertices\\
\hline
The Values of The SuperHyperEdges&The maximum Values of Its Endpoints \\
\hline
\end{tabular}
\label{134TBL1}
\end{table}
\end{definition}

\section{Neutrosophic SuperHyperCycle But As The Extensions Except From Eulerian And Hamiltonian Forms}
The extreme SuperHyperNotion, namely, extreme SuperHyperCycle, is up. Thus the non-obvious extreme SuperHyperCycle, $S$ is up. The extreme type-SuperHyperSet of the extreme SuperHyperCycle, is: $S$ is a extreme SuperHyperSet, is: $S$ does includes only more than four extreme SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the extreme type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``extreme SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] extreme type-SuperHyperSets called the
\begin{center}
\underline{\textbf{SuperHyperCycle}},
\end{center}
is only and only
$S$ in a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ with a illustrated SuperHyperModeling. But all only obvious[non-obvious] simple[non-simple] extreme type-SuperHyperSets of the obvious[non-obvious] simple[non-simple] extreme SuperHyperCycle amid those type-SuperHyperSets, are $S.$ A connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ as a linearly-over-packed SuperHyperModel is featured on the Figures.
\begin{example}\label{134EXM1}
Assume the SuperHyperGraphs in the Figures \eqref{134NSHG1}, \eqref{134NSHG2}, \eqref{134NSHG3}, \eqref{134NSHG4}, \eqref{134NSHG5}, \eqref{134NSHG6}, \eqref{134NSHG7}, \eqref{134NSHG8}, \eqref{134NSHG9}, \eqref{134NSHG10}, \eqref{134NSHG11}, \eqref{134NSHG12}, \eqref{134NSHG13}, \eqref{134NSHG14}, \eqref{134NSHG15}, \eqref{134NSHG16}, \eqref{134NSHG17}, \eqref{134NSHG18}, \eqref{134NSHG19}, and \eqref{134NSHG20}.
\begin{itemize}
\item On the Figure \eqref{134NSHG1}, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperCycle, is up. $E_1$ and $E_3$ are some empty neutrosophic
SuperHyperEdges but $E_2$ is a loop neutrosophic SuperHyperEdge and $E_4$ is a neutrosophic SuperHyperEdge. Thus in the terms of neutrosophic SuperHyperNeighbor, there's only one neutrosophic SuperHyperEdge, namely, $E_4.$ The neutrosophic SuperHyperVertex, $V_3$ is neutrosophic isolated means that there's no neutrosophic SuperHyperEdge has it as a neutrosophic endpoint. Thus the neutrosophic SuperHyperVertex, $V_3,$ \underline{\textbf{is}} excluded in every given neutrosophic SuperHyperCycle.
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is a \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices. There are \underline{less than} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
\underline{\textbf{Isn't}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle, but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices, given by that neutrosophic type-SuperHyperSet; and it's called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a \underline{\textbf{neutrosophic SuperHyperCycle}}. Since it \underline{\textbf{has}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There are only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Thus the obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}

\item On the Figure \eqref{134NSHG2}, the SuperHyperNotion, namely, SuperHyperCycle, is up. $E_1,E_2$ and $E_3$ are some empty SuperHyperEdges but $E_2$ isn't a loop SuperHyperEdge and $E_4$ is a SuperHyperEdge. Thus in the terms of SuperHyperNeighbor, there's only one SuperHyperEdge, namely, $E_4.$ The SuperHyperVertex, $V_3$ is isolated means that there's no SuperHyperEdge has it as an endpoint. Thus the neutrosophic SuperHyperVertex, $V_3,$ \underline{\textbf{is}} excluded in every given neutrosophic SuperHyperCycle.
Thus the neutrosophic SuperHyperVertex, $V_3,$ \underline{\textbf{is}} excluded in every given neutrosophic SuperHyperCycle.
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is a \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices. There are \underline{less than} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
\underline{\textbf{Isn't}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle, but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices, given by that neutrosophic type-SuperHyperSet; and it's called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a \underline{\textbf{neutrosophic SuperHyperCycle}}. Since it \underline{\textbf{has}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There are only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Thus the obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_2\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}

\item On the Figure \eqref{134NSHG3}, the SuperHyperNotion, namely, SuperHyperCycle, is up. $E_1,E_2$ and $E_3$ are some empty SuperHyperEdges but $E_4$ is a SuperHyperEdge. Thus in the terms of SuperHyperNeighbor, there's only one SuperHyperEdge, namely, $E_4.$ $E_2$ is an isolated SuperHyperEdge.
\\
With the exception of $E_2$, the concept could be applied. With keeping $E_2$ in the mind, the story is coming up.
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is a \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices. There are \underline{less than} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
\underline{\textbf{Isn't}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle, but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices, given by that neutrosophic type-SuperHyperSet; and it's called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a \underline{\textbf{neutrosophic SuperHyperCycle}}. Since it \underline{\textbf{has}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There are only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Thus the obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{E_4\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_1,V_2,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=z~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}

\item On the Figure \eqref{134NSHG4}, the SuperHyperNotion, namely, a SuperHyperCycle, is up. There's no empty SuperHyperEdge but $E_3$ are a loop SuperHyperEdge on $\{F\},$ and there are some SuperHyperEdges, namely, $E_1$ on $\{H,V_1,V_3\},$ alongside $E_2$ on $\{O,H,V_4,V_3\}$ and $E_4,E_5$ on $\{N,V_1,V_2,V_3,F\}.$
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is a \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices. There are \underline{less than} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
\underline{\textbf{Isn't}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle, but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices, given by that neutrosophic type-SuperHyperSet; and it's called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a \underline{\textbf{neutrosophic SuperHyperCycle}}. Since it \underline{\textbf{has}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There are only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Thus the obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)=\{V_3,E_1,V_4,E_2,H,E_1,V_3\}~\text{is a neutrosophic SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^3~\text{is a neutrosophic SuperHyperCycle SuperHyperPolynomial.}
\\&&
\mathcal{C}(NSHG)=\{V_3,V_4,H,V_3\}~\text{is a neutrosophic R-SuperHyperCycle.}
\\&&
\mathcal{C}(NSHG)=4z^4~{\small\text{is a neutrosophic R-SuperHyperCycle SuperHyperPolynomial.}}
\end{eqnarray*}
\item On the Figure \eqref{134NSHG5}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
Is a \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices. There are \underline{less than} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
\underline{\textbf{Isn't}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle, but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices, given by that neutrosophic type-SuperHyperSet; and it's called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a \underline{\textbf{neutrosophic SuperHyperCycle}}. Since it \underline{\textbf{has}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There are only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
Thus the obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle}}=\{V_5,E_1,V_4,E_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}}=2z^2.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle}}=\{V_5,V_4,V_5\}.
\\&&
\mathcal{C}(NSHG)_{\text{Neutrosophic Quasi-R-SuperHyperCycle SuperHyperPolynomial}}=2z^3.
\end{eqnarray*}

\item On the Figure \eqref{134NSHG6}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge.
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
Is a \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices. There are \underline{more than} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle, but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices, given by that neutrosophic type-SuperHyperSet; and it's called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a \underline{\textbf{neutrosophic SuperHyperCycle}}. Since it \underline{\textbf{has}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There aren't only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
Is up. The non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
Doesn't include only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}= \{V_i,E_i,V_{i+1}\}_{i=1}^{21}\cup\{V_{22},E_{32},V_i,E_{i+11},E_{11},V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=11z^{22}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\\&&
\{V_i,V_{i+1}\}_{i=1}^{21}\\&&\cup\{V_{22},V_i,V_1\}_{j=21-j}^{9}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=11z^{23}.
\end{eqnarray*}
\item On the Figure \eqref{134NSHG7}, the SuperHyperNotion, namely, SuperHyperCycle, is up.
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
Is a \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices. There are \underline{more than} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle, but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices, given by that neutrosophic type-SuperHyperSet; and it's called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a \underline{\textbf{neutrosophic SuperHyperCycle}}. Since it \underline{\textbf{has}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There aren't only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
Is up. The non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
Doesn't include only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_8,E_{17},V_{14},E_{12},V_{12},E_{15},V_3,E_3,V_4,E_{16},V_7,E_7,V_8\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=6z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_8,V_{14},V_{12},V_3,V_4,V_7,V_8\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=6z^{7}.
\end{eqnarray*}
\item On the Figure \eqref{134NSHG8}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is a \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices. There are \underline{less than} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Does has less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
\underline{\textbf{Isn't}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle, but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices, given by that neutrosophic type-SuperHyperSet; and it's called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a \underline{\textbf{neutrosophic SuperHyperCycle}}. Since it \underline{\textbf{has}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There are only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Thus the obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}= \{\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ of dense SuperHyperModel as the Figure \eqref{134NSHG8}.
\item On the Figure \eqref{134NSHG9}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. There's no coverage on either all SuperHyperVertices or all SuperHyperEdges. Thus the quasi-discussion on the intended notion is up. Disclaimer: The terms are in this item are referred to the prefix ``quasi'' since the notion isn't seen and applied totally but somehow the coincidence is achieved in the terms of neither of all SuperHyperVertices or all SuperHyperEdges in any coverage. Thus the terms Neutrosophic SuperHyperCycle, Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial, Neutrosophic R-Quasi-SuperHyperCycle, and Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial are up even neither of the analogous terms have the prefix `quasi'' and even more all the context are about the quasi-style of the studied notion and the used notion is quasi-notion even they're addressed without the term ``quasi''. Furthermore, for the convenient usage and the harmony of the context with the used title and other applied segments , the term ``quasi'' isn't used more than the following groups of expressions.
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
Is a \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices. There aren't \underline{less than} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle, but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There's no neutrosophic SuperHyperCycle such that it has all neutrosophic SuperHyperVertices, given by that neutrosophic type-SuperHyperSet; and it's called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a \underline{\textbf{neutrosophic SuperHyperCycle}}. Since it \underline{\textbf{has}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle but it has either all neutrosophic SuperHyperEdges or all neutrosophic SuperHyperVertices and in this case, it has all neutrosophic SuperHyperEdges. There aren't only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
Is up. The non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
Doesn't include only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple[non-simple] neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=\\&& \{V_i,E_i,V_6,E_{17},V_{16},d_1,V_1\}_{i=2}^{5}\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_1,V_i,V_{16},V_1\}_{i=2}^{6}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=11z^{8}.
\end{eqnarray*}
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ of highly-embedding-connected SuperHyperModel as the Figure \eqref{134NSHG9}.
\item On the Figure \eqref{134NSHG10}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. There's no coverage on either all SuperHyperVertices or all SuperHyperEdges. Thus the quasi-discussion on the intended notion is up. Disclaimer: The terms are in this item are referred to the prefix ``quasi'' since the notion isn't seen and applied totally but somehow the coincidence is achieved in the terms of neither of all SuperHyperVertices or all SuperHyperEdges in any coverage. Thus the terms Neutrosophic SuperHyperCycle, Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial, Neutrosophic R-Quasi-SuperHyperCycle, and Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial are up even neither of the analogous terms have the prefix `quasi'' and even more all the context are about the quasi-style of the studied notion and the used notion is quasi-notion even they're addressed without the term ``quasi''. Furthermore, for the convenient usage and the harmony of the context with the used title and other applied segments , the term ``quasi'' isn't used more than the following groups of expressions.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
Is an \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are \underline{not} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
Does has less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a neutrosophic \underline{\textbf{ SuperHyperCycle}}. Since it\underline{\textbf{'s}}   \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_{14},E_4,V_{12},E_6,V_{13},E_7,V_{14}\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^3.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_{14}V_{12},V_{13},V_{14}\}
\\&& \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^4.
\end{eqnarray*}
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ of dense SuperHyperModel as the Figure \eqref{134NSHG10}.
\item On the Figure \eqref{134NSHG11}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
Is an \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are \underline{not} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
Does has less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a neutrosophic \underline{\textbf{ SuperHyperCycle}}. Since it\underline{\textbf{'s}}   \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is not:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is not:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_6,V_5,E_5,V_6,E_4,V_4,E_7,V_2,E_1,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=3z^5.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\\&&
\{V_1,V_5,V_6,V_4,V_2,V_1\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=3z^6.
\end{eqnarray*}
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$
\item On the Figure \eqref{134NSHG12}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. There's only one neutrosophic SuperHyperEdges between any given neutrosophic amount of neutrosophic SuperHyperVertices. Thus there isn't any neutrosophic SuperHyperCycle at all.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is an \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are \underline{not} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Does has less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a neutrosophic \underline{\textbf{ SuperHyperCycle}}. Since it\underline{\textbf{'s}}   \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is not:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is not:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=
\{\}
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$
\item On the Figure \eqref{134NSHG13}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.   The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
Is an \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are \underline{not} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
Does has less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a neutrosophic \underline{\textbf{ SuperHyperCycle}}. Since it\underline{\textbf{'s}}   \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is not:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is not:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle}=
\\&&
\{V_1,E_1,V_2,E_{10},V_3,E_8,V_6,E_4,V_4,E_2,V_5,E_6,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic SuperHyperCycle SuperHyperPolynomial}=z^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle}=\{V_i\}_{i=1}^6.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-SuperHyperCycle SuperHyperPolynomial}=z^6.
\end{eqnarray*}
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$
\item On the Figure \eqref{134NSHG14}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0
\end{eqnarray*}
is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.   The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is an \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are \underline{not} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a neutrosophic \underline{\textbf{ SuperHyperCycle}}. Since it\underline{\textbf{'s}}   \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's noted that this neutrosophic SuperHyperGraph $ESHG:(V,E)$ is an neutrosophic graph $G:(V,E)$ thus the notions in both settings are coincided.
\item On the Figure \eqref{134NSHG15}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0
\end{eqnarray*}
is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.   The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is an \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are \underline{not} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Doesn't have less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a neutrosophic \underline{\textbf{ SuperHyperCycle}}. Since it\underline{\textbf{'s}}   \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are not only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Is the neutrosophic SuperHyperSet, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=0.
\end{eqnarray*}
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's noted that this neutrosophic SuperHyperGraph $ESHG:(V,E)$ is an neutrosophic graph $G:(V,E)$ thus the notions in both settings are coincided.
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ as Linearly-Connected SuperHyperModel On the Figure \eqref{134NSHG15}.
\item On the Figure \eqref{134NSHG16}, the SuperHyperNotion, namely, SuperHyperCycle, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.   The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle.
The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
Is the neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
Is an \underline{\textbf{Neutrosophic SuperHyperCycle}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive sequence of the neutrosophic SuperHyperVertices and the neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are \underline{not} only \underline{\textbf{four}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperCycle isn't up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only less than \underline{\textbf{four}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
Does has less than four SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle \underline{\textbf{isn't}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices],
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
Is a neutrosophic SuperHyperCycle $\mathcal{C}(ESHG)$ for a neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices[SuperHyperEdges] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperCycle \underline{\textbf{and}} it's a neutrosophic \underline{\textbf{ SuperHyperCycle}}. Since it\underline{\textbf{'s}}   \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's only one neutrosophic consecutive neutrosophic sequence of neutrosophic SuperHyperVertices and neutrosophic SuperHyperEdges form only one neutrosophic SuperHyperCycle. There are only less than four neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
Thus the non-obvious neutrosophic SuperHyperCycle,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperCycle, is:
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
Does includes only less than four SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only simple neutrosophic type-SuperHyperSet called the
\begin{center}
\underline{\textbf{``neutrosophic SuperHyperCycle''}}
\end{center}
amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the
\begin{center}
\underline{\textbf{Neutrosophic SuperHyperCycle}},
\end{center}
is only and only
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_9,E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{10},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_3,V_{11},E_4,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_8,E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{10},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_3,V_{11},E_4,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_8,E_4,V_{10}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_9,E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_3,V_{11},E_4,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_8,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_3,V_9,E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_3,V_{10},E_4,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_9,E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{10},E_3,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,E_4,V_{11},E_3,V_8\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_8,E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{10},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,E_4,V_{11},E_3,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_8,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_9,E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},E_4,V_{11},E_3,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_8,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},E_4,V_9,E_3,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},E_4,V_{10},E_3,V_{11}\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_4,V_{17},E_5,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_4,V_{15},E_5,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{15},E_5,V_{17},E_4,V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},E_5,V_{15},E_4,V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=28z^2.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_9,V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{10},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_8,V_{11},V_8\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_8,V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{10},V_9\}.
\end{eqnarray*}
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_9,V_{11},V_9\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_8,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_9,V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{10},V_{11},V_{10}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_8,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{11},V_9,V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{11},V_{10},V_{11}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=
\{V_{15}V_{17},V_{15}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_{17},V_{15},V_{17}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=14z^3.
\end{eqnarray*}
In a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$
\item On the Figure \eqref{134NSHG17}, the SuperHyperNotion, namely, SuperHyperCycle, is up. The Algorithm is straightforward.
\item On the Figure \eqref{134NSHG18}, the SuperHyperNotion, namely, SuperHyperCycle, is up. The Algorithm is straightforward.
\item On the Figure \eqref{134NSHG20}, the SuperHyperNotion, namely, SuperHyperCycle, is up. The Algorithm is straightforward.
\end{itemize}
\end{example}
\begin{figure}
\includegraphics[width=100mm]{134NSHG1.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG1}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG2.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG2}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG3.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG3}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG4.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG4}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG5.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG5}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG6.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG6}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG7.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG7}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG8.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG8}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG9.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG9}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG10.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG10}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG11.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG11}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG12.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG12}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG13.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG13}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG14.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG14}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG15.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG15}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG16.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG16}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG17.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG17}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG18.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG18}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG19.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG19}
\end{figure}
\begin{figure}
\includegraphics[width=100mm]{134NSHG20.png}
\caption{The SuperHyperGraphs Associated to the Notions of SuperHyperCycle in the Example \eqref{134EXM1} }
\label{134NSHG20}
\end{figure}
\begin{proposition}
Assume a connected loopless neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then in the worst case, literally,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=z^4.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_1,V_2,V_3,V_4,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=z^5.
\end{eqnarray*}
Is a neutrosophic type-result-SuperHyperCycle. In other words, the least cardinality, the lower sharp bound for the cardinality, of a neutrosophic type-result-SuperHyperCycle is the cardinality of
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_1,E_1,V_2,E_2,V_3,E_3,V_4,E_4,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}=z^4.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}=\{V_1,V_2,V_3,V_4,V_1\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=z^5.
\end{eqnarray*}
\end{proposition}
\begin{proposition}
Assume a simple neutrosophic SuperHyperGraph $ESHG:(V,E).$ Then the neutrosophic number of type-result-R-SuperHyperCycle has, the least neutrosophic cardinality, the lower sharp neutrosophic bound for neutrosophic cardinality, is the neutrosophic cardinality of
$$V\setminus V\setminus\left\{a_{E},b_{E'},c_{E''},c_{E'''}\right\}_{E=\left\{E\in E_{ESHG:(V,E)}~|~|E|=\max\left\{|E|~|~E\in E_{ESHG:(V,E)}\right\}\right\}}.$$
If there's a neutrosophic type-result-R-SuperHyperCycle with the least neutrosophic cardinality, the lower sharp neutrosophic bound for cardinality.
\end{proposition}

\section{The Departures on The Theoretical Results Toward Theoretical Motivations}
The previous neutrosophic approaches apply on the upcoming neutrosophic results on neutrosophic SuperHyperClasses.
\begin{proposition}
Assume a connected neutrosophic SuperHyperPath $ESHP:(V,E).$ Then
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}
\\&&=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}
\\&&=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=az^{s}+bz^{t}.
\end{eqnarray*}
\end{proposition}
\begin{proof}
Let $P:V_1,E_1,V_2,E_2,\ldots,V_z$ is a longest path taken from a connected neutrosophic SuperHyperPath $ESHP:(V,E).$ Then there's no cycle. Thus the notion of quasi is up. The latter is straightforward.
\end{proof}
\begin{example}\label{134EXM18a}
In the Figure \eqref{134NSHG18a}, the connected neutrosophic SuperHyperPath $ESHP:(V,E),$ is highlighted and featured. The neutrosophic SuperHyperSet, in the neutrosophic SuperHyperModel \eqref{134NSHG18a}, is the SuperHyperCycle.
\begin{figure}
\includegraphics[width=100mm]{134NSHG18.png}
\caption{a neutrosophic SuperHyperPath Associated to the Notions of neutrosophic SuperHyperCycle in the Example \eqref{134EXM18a}}
\label{134NSHG18a}
\end{figure}
\end{example}

\begin{proposition}
Assume a connected neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}
\\&&=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}
\\&&=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=az^{s}+bz^{t}.
\end{eqnarray*}
\end{proposition}
\begin{proof}
Let $C:V_1,E_1,V_2,E_2,\ldots,V_z$ is a longest cycle taken from a connected neutrosophic SuperHyperCycle $ESHC:(V,E).$ Then there's at least one cycle. Thus the notion of quasi isn't up and the SuperHyperNotions based on SuperHyperCycle could be applied. The latter is straightforward.
\end{proof}
\begin{example}\label{134EXM19a}
In the Figure \eqref{134NSHG19a}, the connected neutrosophic SuperHyperCycle $NSHC:(V,E),$ is highlighted and featured. The obtained neutrosophic SuperHyperSet, in the neutrosophic SuperHyperModel \eqref{134NSHG19a},
is the neutrosophic SuperHyperCycle.
\begin{figure}
\includegraphics[width=100mm]{134NSHG19.png}
\caption{a neutrosophic SuperHyperCycle Associated to the neutrosophic Notions of neutrosophic SuperHyperCycle in the neutrosophic Example \eqref{134EXM19a}}
\label{134NSHG19a}
\end{figure}
\end{example}
\begin{proposition}
Assume a connected neutrosophic SuperHyperStar $ESHS:(V,E).$ Then
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}
\\&&=\{E\in E_{ESHG:(V,E)}\}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}
\\&&=\sum_{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}z^{|E|_{\text{Neutrosophic Cardinality}}~|~E:\in E_{ESHG:(V,E)}}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t},\ldots.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=z^{s}+z^{t}+,\ldots.
\end{eqnarray*}
\end{proposition}
\begin{proof}
Let $P:V_1,E_1,V_2,E_2,\ldots,V_z$ is a longest path taken from a connected neutrosophic SuperHyperStar $ESHS:(V,E).$ Then there's no cycle. Thus the notion of quasi is up. The latter is straightforward.
\end{proof}

\begin{example}\label{134EXM20a}
In the Figure \eqref{134NSHG20a}, the connected neutrosophic SuperHyperStar $ESHS:(V,E),$ is highlighted and featured. The obtained neutrosophic SuperHyperSet, by the Algorithm in previous neutrosophic result, of the neutrosophic SuperHyperVertices of the connected neutrosophic SuperHyperStar $ESHS:(V,E),$ in the neutrosophic SuperHyperModel \eqref{134NSHG20a}, is the neutrosophic SuperHyperCycle.
\begin{figure}
\includegraphics[width=100mm]{134NSHG20.png}
\caption{a neutrosophic SuperHyperStar Associated to the neutrosophic Notions of neutrosophic SuperHyperCycle in the neutrosophic Example \eqref{134EXM20a}}
\label{134NSHG20a}
\end{figure}
\end{example}
\begin{proposition}
Assume a connected neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}
\\&&=\{E_{2i-1}\}_{i=1}^{\min|P_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}
\\&&=z^{\min|P_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}. \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_i\}_{i=1}^{s}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=az^{s}.
\end{eqnarray*}
\end{proposition}
\begin{proof}
Let $C:V_1,E_1,V_2,E_2,\ldots,V_z$ is a longest cycle taken from a connected neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then there's at least one cycle. Thus the notion of quasi isn't up and the SuperHyperNotions based on SuperHyperCycle could be applied. There are only two SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the $C:V_1,E_1,V_2,E_2,\ldots,V_z$ is a longest cycle taken from a connected neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Thus only four SuperHyperVertices and only four SuperHyperEdges are attained in any solution $C:V_1,E_1,V_2,E_2,\ldots,V_z.$ The latter is straightforward.
\end{proof}
\begin{example}\label{134EXM21a}
In the neutrosophic Figure \eqref{134NSHG21a}, the connected neutrosophic SuperHyperBipartite $ESHB:(V,E),$ is neutrosophic highlighted and neutrosophic featured. The obtained neutrosophic SuperHyperSet, by the neutrosophic Algorithm in previous neutrosophic result, of the neutrosophic SuperHyperVertices of the connected neutrosophic SuperHyperBipartite $ESHB:(V,E),$ in the neutrosophic SuperHyperModel \eqref{134NSHG21a}, is the neutrosophic SuperHyperCycle.
\begin{figure}
\includegraphics[width=100mm]{134NSHG21.png}
\caption{a neutrosophic SuperHyperBipartite neutrosophic Associated to the neutrosophic Notions of neutrosophic SuperHyperCycle in the Example \eqref{134EXM21a}}
\label{134NSHG21a}
\end{figure}
\end{example}
\begin{proposition}
Assume a connected neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}
\\&&=\{E_{2i-1}\}_{i=1}^{\min|P_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}
\\&&=z^{\min|P_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}. \\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_i\}_{i=1}^{s}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=az^{s}.
\end{eqnarray*}
\end{proposition}
\begin{proof}
Let $C:V_1,E_1,V_2,E_2,\ldots,V_z$ is a longest cycle taken from a connected neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Then there's at least one cycle. Thus the notion of quasi isn't up and the SuperHyperNotions based on SuperHyperCycle could be applied. There are only $z'$ SuperHyperParts. Thus every SuperHyperPart could have one SuperHyperVertex as the representative in the $C:V_1,E_1,V_2,E_2,\ldots,V_z$ is a connected neutrosophic SuperHyperMultipartite $ESHM:(V,E).$ Thus only $z'$ SuperHyperVertices and only $z'$ SuperHyperEdges are attained in any solution $C:V_1,E_1,V_2,E_2,\ldots,V_z.$ The latter is straightforward.
\end{proof}

\begin{example}\label{134EXM22a}
In the Figure \eqref{134NSHG22a}, the connected neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ is highlighted and neutrosophic featured. The obtained neutrosophic SuperHyperSet, by the Algorithm in previous neutrosophic result, of the neutrosophic SuperHyperVertices of the connected neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the neutrosophic SuperHyperModel \eqref{134NSHG22a}, is the neutrosophic SuperHyperCycle.
\begin{figure}
\includegraphics[width=100mm]{134NSHG22.png}
\caption{a neutrosophic SuperHyperMultipartite Associated to the Notions of neutrosophic SuperHyperCycle in the Example \eqref{134EXM22a}}
\label{134NSHG22a}
\end{figure}
\end{example}
\begin{proposition}
Assume a connected neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then,
\begin{eqnarray*}
&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle}
\\&&=\{E_{2i-1}\}_{i=1}^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic Quasi-SuperHyperCycle SuperHyperPolynomial}
\\&&=2z^{\lfloor\frac{|E_{ESHG:(V,E)}|_{\text{Neutrosophic Cardinality}}}{2}\rfloor}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle}=\{V_i\}_{i=1}^{s},\{V_j\}_{j=1}^{t}.
\\&&
\mathcal{C}(NSHG)_{Neutrosophic R-Quasi-SuperHyperCycle SuperHyperPolynomial}=az^{s}+bz^{t}.
\end{eqnarray*}
\end{proposition}
\begin{proof}
Let $C:V_1,E_1,V_2,E_2,\ldots,V_z$ is a longest cycle taken from a connected neutrosophic SuperHyperWheel $ESHW:(V,E).$ Then there's at least one cycle. Thus the notion of quasi isn't up and the SuperHyperNotions based on SuperHyperCycle could be applied. The unique embedded SuperHyperCycle proposes some longest cycles excerpt from some representatives. The latter is straightforward.
\end{proof}
\begin{example}\label{134EXM23a}
In the neutrosophic Figure \eqref{134NSHG23a}, the connected neutrosophic SuperHyperWheel $NSHW:(V,E),$ is neutrosophic highlighted and featured. The obtained neutrosophic SuperHyperSet, by the Algorithm in previous result, of the neutrosophic SuperHyperVertices of the connected neutrosophic SuperHyperWheel $ESHW:(V,E),$
in the neutrosophic SuperHyperModel \eqref{134NSHG23a}, is the neutrosophic SuperHyperCycle.
\begin{figure}
\includegraphics[width=100mm]{134NSHG23.png}
\caption{a neutrosophic SuperHyperWheel neutrosophic Associated to the neutrosophic Notions of neutrosophic SuperHyperCycle in the neutrosophic Example \eqref{134EXM23a}}
\label{134NSHG23a}
\end{figure}
\end{example}

\section{Background}
There are some researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them.
\\
First article is titled ``properties of SuperHyperGraph and neutrosophic SuperHyperGraph'' in \textbf{Ref.} \cite{HG1} by Henry Garrett (2022). It's first step toward the research on neutrosophic SuperHyperGraphs. This research article is published on the journal ``Neutrosophic Sets and Systems'' in issue 49 and the pages 531-561. In this research article, different types of notions like dominating, resolving, coloring, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alliance, and global-powerful alliance are defined in SuperHyperGraph and neutrosophic SuperHyperGraph. Some Classes of SuperHyperGraph and Neutrosophic SuperHyperGraph are cases of research. Some results are applied in family of SuperHyperGraph and neutrosophic SuperHyperGraph. Thus this research article has concentrated on the vast notions and introducing the majority of notions.
\\
The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs'' in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It's published in prestigious and fancy journal is entitled “Journal of Current Trends in Computer Science Research (JCTCSR)” with abbreviation ``J Curr Trends Comp Sci Res'' in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It's the breakthrough toward independent results based on initial background.
\\
The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes'' in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It's published in prestigious and fancy journal is entitled “Journal of Mathematical Techniques and Computational Mathematics(JMTCM)” with abbreviation ``J Math Techniques Comput Math'' in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It's the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers.
\\
In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph'' in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022), ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs'' in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022), ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer’s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer’s Recognition'' in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer’s Recognition On Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer’s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph'' in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer’s Recognition Applied in (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer’s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer's Circumstances Where Cancer's Recognition Titled (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints'' in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer’s Neutrosophic Recognition And Beyond'' in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperStable on Cancer’s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs
'' in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints'' in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints'' in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer’s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances'' in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer’s Recognitions And Related (Neutrosophic) SuperHyperClasses'' in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer’s Recognitions'' in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer’s Treatments'' in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses'' in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer’s Recognition In Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer's Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer's Recognition in the Perfect Connections of Cancer's Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer's Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer's Recognition called Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer's Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer's Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique'' in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer’s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer's Recognition Titled (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints'' in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer’s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer’s Neutrosophic Recognition And Beyond'' in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph'' in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)'' in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022), there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.
\\
Some studies and researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 2732 readers in Scribd. It's titled ``Beyond Neutrosophic Graphs'' and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory.
\\
Also, some studies and researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3504 readers in Scribd. It's titled ``Neutrosophic Duality'' and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It's smart to consider a set but acting on its complement that what's done in this research book which is popular in the terms of high readers in Scribd.
\\
See the seminal researches \cite{HG1,HG2,HG3}. The formalization of the notions on the framework of Extreme SuperHyperCycle theory, Neutrosophic SuperHyperCycle theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38}. Two popular research books in Scribd in the terms of high readers, 2638 and 3363 respectively, on neutrosophic science is on \cite{HG39,HG40}.
\begin{thebibliography}{595}

\bibitem{HG1} Henry Garrett, ``\textit{Properties of SuperHyperGraph and Neutrosophic SuperHyperGraph}'', Neutrosophic Sets and Systems 49 (2022) 531-561 (doi: 10.5281/zenodo.6456413). (http://fs.unm.edu/NSS/NeutrosophicSuperHyperGraph34.pdf). (https://digitalrepository.unm.edu/nss\_journal/vol49/iss1/34).

\bibitem{HG2} Henry Garrett, ``\textit{Neutrosophic Co-degree and Neutrosophic Degree alongside Chromatic Numbers in the Setting of Some Classes Related to Neutrosophic Hypergraphs}'', J Curr Trends Comp Sci Res 1(1) (2022) 06-14.

\bibitem{HG3} Henry Garrett, ``\textit{Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes}'', J Math Techniques Comput Math 1(3) (2022) 242-263.

\bibitem{HG4}
Garrett, Henry. ``\textit{0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph.}'' CERN European Organization for Nuclear Research - Zenodo, Nov. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.5281/zenodo.6319942.
https://oa.mg/work/10.5281/zenodo.6319942

\bibitem{HG5}
Garrett, Henry. ``\textit{0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs.}'' CERN European Organization for Nuclear Research - Zenodo, Feb. 2022. CERN European Organization for Nuclear Research, https://doi.org/10.13140/rg.2.2.35241.26724.
https://oa.mg/work/10.13140/rg.2.2.35241.26724

\bibitem{HG6}
Henry Garrett, ``\textit{Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer’s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs}'', Preprints 2023, 2023010308 (doi: 10.20944/preprints202301.0308.v1).

\bibitem{HG7}
Henry Garrett, ``\textit{Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer’s Recognition}'', Preprints 2023, 2023010282 (doi: 10.20944/preprints202301.0282.v1).

\bibitem{HG8}
Henry Garrett, ``\textit{Neutrosophic Version Of Separates Groups Of Cells In Cancer’s Recognition On Neutrosophic SuperHyperGraphs}'', Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).

\bibitem{HG9}
Henry Garrett, ``\textit{The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer’s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph}'', Preprints 2023, 2023010265 (doi: 10.20944/preprints202301.0265.v1).

\bibitem{HG10}
Henry Garrett, ``\textit{Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer’s Recognition Applied in (Neutrosophic) SuperHyperGraphs}'', Preprints 2023, 2023010262,(doi: 10.20944/preprints202301.0262.v1).

\bibitem{HG11}
Henry Garrett, ``\textit{Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer’s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs}'', Preprints 2023, 2023010240 (doi: 10.20944/preprints202301.0240.v1).

\bibitem{HG12}
Henry Garrett, ``\textit{Extremism of the Attacked Body Under the Cancer's Circumstances Where Cancer's Recognition Titled (Neutrosophic) SuperHyperGraphs}'', Preprints 2023, 2023010224, (doi: 10.20944/preprints202301.0224.v1).

\bibitem{HG13}
Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs}'', Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1).

\bibitem{HG14}
Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints}'', Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1).

\bibitem{HG15}
Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer’s Neutrosophic Recognition And Beyond}'', Preprints 2023, 2023010044

\bibitem{HG16}
Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer’s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs}'', Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1).

\bibitem{HG17} Henry Garrett, \textit{``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs''}, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1).

\bibitem{HG18} Henry Garrett, \textit{``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints''}, Preprints 2023, 2023010088 (doi: 10.20944/preprints202301.0088.v1).

\bibitem{HG19} Henry Garrett, \textit{``(Neutrosophic) SuperHyperModeling of Cancer’s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances''}, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1).

\bibitem{HG20} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer’s Recognitions And Related (Neutrosophic) SuperHyperClasses}'', Preprints 2022, 2022120540 (doi: 10.20944/preprints202212.0540.v1).

\bibitem{HG21} Henry Garrett, ``\textit{SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer’s Recognitions}'', Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1).

\bibitem{HG22} Henry Garrett, ``\textit{Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer’s Treatments}'', Preprints 2022, 2022120324 (doi: 10.20944/preprints202212.0324.v1).

\bibitem{HG23} Henry Garrett, ``\textit{SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses}'', Preprints 2022, 2022110576 (doi: 10.20944/preprints202211.0576.v1).

\bibitem{HG24} Henry Garrett,``\textit{SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer’s Recognition In Neutrosophic SuperHyperGraphs}'', ResearchGate 2023,(doi: 10.13140/RG.2.2.35061.65767).

\bibitem{HG25} Henry Garrett,``\textit{The Focus on The Partitions Obtained By Parallel Moves In The Cancer's Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs}'', ResearchGate 2023, (doi: 10.13140/RG.2.2.18494.15680).

\bibitem{HG26} Henry Garrett,``\textit{Extreme Failed SuperHyperClique Decides the Failures on the Cancer's Recognition in the Perfect Connections of Cancer's Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs}'', ResearchGate 2023, (doi: 10.13140/RG.2.2.32530.73922).

\bibitem{HG27} Henry Garrett,``\textit{Indeterminacy On The All Possible Connections of Cells In Front of Cancer's Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer's Recognition called Neutrosophic SuperHyperGraphs}'', ResearchGate 2023, (doi: 10.13140/RG.2.2.15897.70243).

\bibitem{HG28} Henry Garrett,``\textit{Perfect Directions Toward Idealism in Cancer's Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs}'', ResearchGate 2023, (doi: 10.13140/RG.2.2.30092.80004).

\bibitem{HG29} Henry Garrett,``\textit{Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer's Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique}'', ResearchGate 2023, (doi: 10.13140/RG.2.2.23172.19849).

\bibitem{HG30} Henry Garrett,``\textit{Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer’s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs}'', ResearchGate 2023, (doi: 10.13140/RG.2.2.17385.36968).

\bibitem{HG31} Henry Garrett, ``\textit{Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer's Recognition Titled (Neutrosophic) SuperHyperGraphs}'', ResearchGate 2023, (doi: 10.13140/RG.2.2.28945.92007).

\bibitem{HG32} Henry Garrett, ``\textit{Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints}'', ResearchGate 2023, (doi: 10.13140/RG.2.2.11447.80803).

\bibitem{HG33} Henry Garrett, ``\textit{(Neutrosophic) SuperHyperStable on Cancer’s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs}'', ResearchGate 2023, (doi: 10.13140/RG.2.2.35774.77123).

\bibitem{HG34} Henry Garrett, ``\textit{Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer’s Neutrosophic Recognition And Beyond}'', ResearchGate 2022, (doi: 10.13140/RG.2.2.36141.77287).

\bibitem{HG35} Henry Garrett, ``\textit{(Neutrosophic) 1-Failed SuperHyperForcing in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs}'', ResearchGate 2022, (doi: 10.13140/RG.2.2.29430.88642).

\bibitem{HG36} Henry Garrett, ``\textit{Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs}'', ResearchGate 2022, (doi: 10.13140/RG.2.2.11369.16487).

\bibitem{HG37} Henry Garrett, \textit{``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph''}, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244).

\bibitem{HG38} Henry Garrett, ``\textit{Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)}'', ResearchGate 2022 (doi: 10.13140/RG.2.2.25385.88160).

\bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}'', Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf).

\bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}'', Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf).

\end{thebibliography}
\end{document}

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New Research On Cancer's Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV

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