Published April 6, 2023 | Version v1
Journal article Open

New Ideas On Super Nebulous By Hyper Nebbish Of Hamiltonian-Type-Cycle-Neighbor In Cancer's Recognition With (Neutrosophic) SuperHyperGraph

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

Description

\documentclass[10pt,letterpaper]{article}
\usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry}
\usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color}
\usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref}
% use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts)
\usepackage[utf8]{inputenc}

% clean citations
\usepackage{cite}

% hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url
\usepackage{nameref,hyperref}

% line numbers
\usepackage[right]{lineno}

% improves typesetting in LaTeX
\usepackage{microtype}
\DisableLigatures[f]{encoding = *, family = * }

% text layout - change as needed
\raggedright
\setlength{\parindent}{0.5cm}
\textwidth 5.25in
\textheight 8.79in

% Remove % for double line spacing
%\usepackage{setspace}
%\doublespacing

% use adjustwidth environment to exceed text width (see examples in text)
\usepackage{changepage}

% adjust caption style
\usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption}

% remove brackets from references
\makeatletter
\renewcommand{\@biblabel}[1]{\quad#1.}
\makeatother

% headrule, footrule and page numbers
\usepackage{lastpage,fancyhdr,graphicx}
\usepackage{epstopdf}
\pagestyle{myheadings}
\pagestyle{fancy}
\fancyhf{}
\rfoot{\thepage/\pageref{LastPage}}
\renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}}
\fancyheadoffset[L]{2.25in}
\fancyfootoffset[L]{2.25in}

% use \textcolor{color}{text} for colored text (e.g. highlight to-do areas)
\usepackage{color}

% define custom colors (this one is for figure captions)
\definecolor{Gray}{gray}{.25}

% this is required to include graphics
\usepackage{graphicx}

% use if you want to put caption to the side of the figure - see example in text
\usepackage{sidecap}
\usepackage{leftidx}
% use for have text wrap around figures
\usepackage{wrapfig}
\usepackage[pscoord]{eso-pic}
\usepackage[fulladjust]{marginnote}
\reversemarginpar
\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{xca}[theorem]{Exercise}
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}
\theoremstyle{observation}
\newtheorem{observation}[theorem]{Observation}
\theoremstyle{question}
\newtheorem{question}[theorem]{Question}
\theoremstyle{problem}
\newtheorem{problem}[theorem]{Problem}
\numberwithin{equation}{section}
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhf{}
\fancyhead[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA }
\fancyfoot[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA }
% document begins here
\begin{document}
\vspace*{0.35in}
\linenumbers
% title goes here:
\begin{flushleft}
{\Large
\textbf\newline{
New Ideas On Super Nebulous By Hyper Nebbish Of Hamiltonian-Type-Cycle-Neighbor In Cancer's Recognition With (Neutrosophic) SuperHyperGraph
}
}
\newline
\newline
Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA
% authors go here:

\end{flushleft}
\section{ABSTRACT}
In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}). Assume a Neutrosophic SuperHyperGraph (NSHG) S is a {\tiny Hamiltonian-Type-Cycle-Neighbor} pair S=(V,E). Consider a Neutrosophic SuperHyperSet V={V1,V2,,Vs} and E={E1,E2,,Ez}. Then either V or E is called Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} if the following expression is called Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} criteria holds
  N(Ea)C:C isa SuperHyperCycle and it hasthe maximum number of SuperHyperVertices;
 Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} if the following expression is called Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} criteria holds
  N(Ea)C:C isa SuperHyperCycle and it hasthe maximum number of SuperHyperVertices;
 and |Ei|NEUTROSOPIC CARDINALITY=|Ej|NEUTROSOPIC CARDINALITY; Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}  if the following expression is called Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} criteria holds
  N(Va)C:C isa SuperHyperCycle and it hasthe maximum number of  SuperHyperVertices;
  Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} if the following expression is called Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} criteria holds
  N(Va)C:C isa SuperHyperCycle and it hasthe maximum number of  SuperHyperVertices;
and |Vi|NEUTROSOPIC CARDINALITY=|Vj|NEUTROSOPIC CARDINALITY; Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. ((Neutrosophic) SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}).
 Assume a Neutrosophic SuperHyperGraph (NSHG) S
is a pair S=(V,E). Consider a Neutrosophic SuperHyperEdge (NSHE) E={V1,V2,,Vs}.
Then E is called an Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and 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 conseNeighborive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}; a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and 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  conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}; an Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} SuperHyperPolynomial  if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and 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 conseNeighborive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and 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 conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme V-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and 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 conseNeighborive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}; a Neutrosophic V-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and 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 conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}; an Extreme V-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and 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 conseNeighborive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and 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 conseNeighborive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}; and the Neutrosophic power is corresponded to its Neutrosophic coefficient.  In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}  and Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and  SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer's Recognition'' are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex'' but the relations amid them all officially called ``SuperHyperEdge''. The frameworks ``SuperHyperGraph'' and ``Neutrosophic SuperHyperGraph'' are chosen and elected to research about ``Cancer's Recognition''. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer's Recognition''. Some avenues are posed to pursue this research. It's also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Assume a SuperHyperGraph. Then δSuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} is a maximal    of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of  SuperHyperNeighbors of sS: there are |SN(s)|>|S(VN(s))|+δ; and |SN(s)|<|S(VN(s))|+δ.
The first Expression, holds if S is an δSuperHyperOffensive. And the second Expression, holds if S is an δSuperHyperDefensive; a Neutrosophic δSuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} is a maximal Neutrosophic     of SuperHyperVertices with maximum Neutrosophic cardinality such that either of the following expressions hold for the Neutrosophic cardinalities of  SuperHyperNeighbors of sS there are: |SN(s)|Neutrosophic>|S(VN(s))|Neutrosophic+δ; and
|SN(s)|Neutrosophic<|S(VN(s))|Neutrosophic+δ.
The first Expression, holds if S is a Neutrosophic δSuperHyperOffensive. And the second Expression, holds if S is a Neutrosophic δSuperHyperDefensive
  It's useful to define a ``Neutrosophic'' version of a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} . Since there's more ways to get type-results to make a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}  more understandable. For the sake of having Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, there's a need to ``redefine'' the notion of a ``SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} ''. 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. Assume a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} . It's redefined a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}  if the mentioned Table holds, concerning, ``The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph'' with the key points,  
``The Values of The Vertices \& The Number of Position in Alphabet'',
``The Values of The SuperVertices\&The maximum Values of Its Vertices'',
``The Values of The Edges\&The maximum Values of Its Vertices'',
``The Values of The HyperEdges\&The maximum Values of Its Vertices'', ``The Values of The SuperHyperEdges\&The maximum Values of Its Endpoints''. To get structural examples and instances, I'm going to introduce the next SuperHyperClass of SuperHyperGraph based on a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} . It's the main. It'll be disciplinary to have the foundation of previous definition in the kind of SuperHyperClass. If there's a need to have all SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} until the SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, then it's officially called a ``SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'' but otherwise, it isn't a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} . There are some instances about the clarifications for the main definition titled a ``SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} ''. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} . For the sake of having a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, there's a need to ``redefine'' the notion of a ``Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'' and a ``Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} ''. 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. Assume a Neutrosophic SuperHyperGraph. It's redefined ``Neutrosophic SuperHyperGraph'' if the intended Table holds. And a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}  are redefined to a ``Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'' if the intended Table holds. It's useful to define ``Neutrosophic'' version of SuperHyperClasses. Since there's more ways to get Neutrosophic type-results to make a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}  more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus  SuperHyperPath,  SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and   SuperHyperWheel, are
``Neutrosophic SuperHyperPath'', ``Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'', ``Neutrosophic SuperHyperStar'', ``Neutrosophic SuperHyperBipartite'', ``Neutrosophic SuperHyperMultiPartite'', and ``Neutrosophic SuperHyperWheel'' if the intended Table holds.  A SuperHyperGraph has a ``Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'' where it's the strongest [the maximum Neutrosophic value from all the SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}  amid the maximum value amid all SuperHyperVertices from a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} .] SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} . A graph is a SuperHyperUniform if it's a SuperHyperGraph and the number of elements of SuperHyperEdges are the same. Assume a Neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. It's SuperHyperPath if it's only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; it's SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} if it's only one SuperVertex as intersection amid two given SuperHyperEdges; it's SuperHyperStar it's only one SuperVertex as intersection amid all SuperHyperEdges;
it's SuperHyperBipartite it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; it's SuperHyperMultiPartite  it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; it's a SuperHyperWheel if it's only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. The SuperHyperModel proposes the specific designs and the specific architectures. The SuperHyperModel is officially called ``SuperHyperGraph'' and ``Neutrosophic SuperHyperGraph''. In this SuperHyperModel, The ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperVertices'' and the common and intended properties between ``specific'' cells and ``specific group'' of cells are SuperHyperModeled as ``SuperHyperEdges''. Sometimes, it's useful to have some degrees of determinacy, indeterminacy, and neutrality to have more precise SuperHyperModel which in this case the SuperHyperModel is called ``Neutrosophic''. In the future research, the foundation will be based on the ``Cancer's Recognition'' and the results and the definitions will be introduced in redeemed ways. The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it's called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn't be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it's said to be Neutrosophic SuperHyperGraph] to have convenient perception on what's happened and what's done. There are some specific models, which are well-known and they've got the names, and some SuperHyperGeneral SuperHyperModels. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,  SuperHyperWheel). The aim is to find either the longest SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}  or the strongest SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}  in those Neutrosophic SuperHyperModels. For the longest SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, called SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and the strongest SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, called Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, some general results are introduced. Beyond that in SuperHyperStar, all possible SuperHyperPaths have only two SuperHyperEdges but it's not enough since it's essential to have at least three SuperHyperEdges to form any style of a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. There isn't any formation of any SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} but literarily, it's the deformation of any SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. It, literarily, deforms and it doesn't form.  A basic familiarity with Neutrosophic  SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.
\ \vspace{4mm}
\textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Cancer's Recognition
   \
\textbf{AMS Subject Classification:} 05C17, 05C22, 05E45
\section{Applied Notions Under The Scrutiny Of The Motivation Of This Scientific Research}
In this scientific research, there are some ideas in the featured frameworks of motivations. I try to bring the motivations in the narrative ways. Some cells have been faced with some attacks from the situation which is caused by the cancer's attacks. In this case, there are some embedded analysis on the ongoing situations which in that, the cells could be labelled as some groups and some groups or individuals have excessive labels which all are raised from the behaviors to overcome the cancer's attacks. In the embedded situations, the individuals of cells and the groups of cells could be considered as ``new groups''. Thus it motivates us to find the proper SuperHyperModels for getting more proper analysis on this messy story. I've found the SuperHyperModels which are officially called ``SuperHyperGraphs'' and ``Extreme SuperHyperGraphs''. In this SuperHyperModel, the cells and the groups of cells are defined as ``SuperHyperVertices'' and the relations between the individuals of cells and the groups of cells are defined as ``SuperHyperEdges''. Thus it's another motivation for us to do research on this SuperHyperModel based on the ``Cancer's Recognition''. Sometimes, the situations get worst. The situation is passed from the certainty and precise style. Thus it's the beyond them. There are three descriptions, namely, the degrees of determinacy, indeterminacy and neutrality, for any object based on vague forms, namely, incomplete data, imprecise data, and uncertain analysis. The latter model could be considered on the previous SuperHyperModel. It's SuperHyperModel. It's SuperHyperGraph but it's officially called ``Extreme SuperHyperGraphs''. The cancer is the disease but the model is going to figure out what's going on this phenomenon. The special case of this disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The recognition of the cancer could help to find some treatments for this disease. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer's Recognition'' and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the forms of alliances' styles with the formation of the design and the architecture are formally called ``  SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'' in the themes of jargons and buzzwords. The prefix ``SuperHyper'' refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.  The recognition of the cancer in the long-term function. The specific region has been assigned by the model [it's called SuperHyperGraph] and the long cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn't be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it's said to be Extreme SuperHyperGraph] to have convenient perception on what's happened and what's done. There are some specific models, which are well-known and they've got the names, and some general models. The moves and the traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by an Extreme SuperHyperPath (-/SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,  SuperHyperWheel). The aim is to find either the optimal   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} or the Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} in those Extreme SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Extreme SuperHyperPath s have only two SuperHyperEdges but it's not enough since it's essential to have at least three SuperHyperEdges to form any style of a SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. There isn't any formation of any SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} but literarily, it's the deformation of any SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. It, literarily, deforms and it doesn't form.
Unknown environment 'question'
Unknown environment '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 ``  SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'' and ``Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'' on ``SuperHyperGraph'' and ``Extreme SuperHyperGraph''. Then the research has taken more motivations to define SuperHyperClasses and to find some connections amid this SuperHyperNotion with other SuperHyperNotions. It motivates us to get some instances and examples to make clarifications about the framework of this research. The general results and some results about some connections are some avenues to make key point of this research, ``Cancer's Recognition'', more understandable and more clear.
\
The framework of this research is as follows. In the beginning, I introduce basic definitions to clarify about preliminaries. In the subsection ``Preliminaries'', initial definitions about SuperHyperGraphs and Extreme SuperHyperGraph are deeply-introduced and in-depth-discussed. The elementary concepts are clarified and illustrated completely and sometimes review literature are applied to make sense about what's going to figure out about the upcoming sections. The main definitions and their clarifications alongside some results about new notions,   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, are figured out in sections ``  SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'' and ``Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}''. In the sense of tackling on getting results and in {\tiny Hamiltonian-Type-Cycle-Neighbor} to make sense about continuing the research, the ideas of SuperHyperUniform and Extreme SuperHyperUniform are introduced and as their consequences, corresponded SuperHyperClasses are figured out to debut what's done in this section, titled ``Results on SuperHyperClasses'' and ``Results on Extreme SuperHyperClasses''. As going back to origin of the notions, there are some smart steps toward the common notions to extend the new notions in new frameworks, SuperHyperGraph and Extreme SuperHyperGraph, in the sections ``Results on SuperHyperClasses'' and ``Results on Extreme SuperHyperClasses''. The starter research about the general SuperHyperRelations and as concluding and closing section of theoretical research are contained in the section ``General Results''. Some general SuperHyperRelations are fundamental and they are well-known as fundamental SuperHyperNotions as elicited and discussed in the sections, ``General Results'',
``  SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'', ``Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'', ``Results on SuperHyperClasses'' and ``Results on Extreme SuperHyperClasses''. There are curious questions about what's done about the SuperHyperNotions to make sense about excellency of this research and going to figure out the word ``best'' as the description and adjective for this research as presented in section, ``  SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}''. The keyword of this research debut in the section ``Applications in Cancer's Recognition'' with two cases and subsections ``Case 1: The Initial Steps Toward SuperHyperBipartite as SuperHyperModel'' and ``Case 2: The Increasing Steps Toward SuperHyperMultipartite as SuperHyperModel''. In the section, ``Open Problems'', there are some scrutiny and discernment on what's done and what's happened in this research in the terms of ``questions'' and ``problems'' to make sense to figure out this research in featured style. The advantages and the limitations of this research alongside about what's done in this research to make sense  and to get sense about what's figured out are included in the section, ``Conclusion and Closing Remarks''.
\section{Extreme Preliminaries Of This Scientific Research On the Redeemed Ways}
In this section, the basic material in this scientific 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 scientific research, is presented. Also, the new ideas and their clarifications are elicited.
Unknown environment 'definition'
Unknown environment 'definition'
Unknown environment 'definition'
Unknown environment 'definition'
Unknown environment 'definition'
Unknown environment 'definition'
If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG).
Unknown environment 'definition'
Unknown environment 'definition'
Unknown environment 'definition'
Unknown environment 'definition'


Unknown environment '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.
Unknown environment '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}

Unknown environment 'definition'

Unknown environment 'definition'
Unknown environment 'definition'

Unknown environment 'definition'

 

\begin{definition}(Different Neutrosophic Types of Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}).\
 Assume a Neutrosophic SuperHyperGraph (NSHG) S is a pair S=(V,E). Consider a Neutrosophic SuperHyperSet V={V1,V2,,Vs} and E={E1,E2,,Ez}. Then either V or E is called
\begin{itemize}
  \item[(i)] \textbf{Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}} if the following expression is called \textbf{Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} criteria} holds
  N(Ea)C:C isa SuperHyperCycle and it hasthe maximum number of  SuperHyperVertices;

\item[(ii)] \textbf{Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}} if the following expression is called \textbf{Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} criteria} holds
  N(Ea)C:C isa SuperHyperCycle and it hasthe maximum number of  SuperHyperVertices;

and |Ei|NEUTROSOPIC CARDINALITY=|Ej|NEUTROSOPIC CARDINALITY;
 \item[(iii)] \textbf{Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}} if the following expression is called \textbf{Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} criteria} holds
  N(Va)C:C isa SuperHyperCycle and it hasthe maximum number of  SuperHyperVertices;

\item[(iv)]  \textbf{Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}} if the following expression is called \textbf{Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} criteria} holds
  N(Va)C:C isa SuperHyperCycle and it hasthe maximum number of  SuperHyperVertices;
and |Vi|NEUTROSOPIC CARDINALITY=|Vj|NEUTROSOPIC CARDINALITY;
\item[(v)] \textbf{Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}} if it's either of Neutrosophic e-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic re-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, Neutrosophic v-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and Neutrosophic rv-SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}.
\end{itemize}
\end{definition}


Unknown environment 'definition'

Unknown environment 'definition'
For the sake of having a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, 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.
Unknown environment '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.
Unknown environment 'definition'
It's useful to define a ``Neutrosophic'' version of a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. Since there's more ways to get type-results to make a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} more Neutrosophicly understandable.
\
For the sake of having a Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, there's a need to ``\textbf{redefine}'' the Neutrosophic notion of ``Neutrosophic SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}''. 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.
Unknown environment 'definition'
\section{
Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} But As The Extensions Excerpt From Dense And Super Forms}
Unknown environment 'definition'
Unknown environment 'definition'
Unknown environment 'definition'
The notion of independent on Extreme Variable is likewise.
Unknown environment 'definition'
Unknown environment 'definition'
\begin{lemma}
 Assume an Extreme SuperHyperGraph (NSHG) S is a pair S=(V,E). Consider S=(V,E) is a probability {\tiny Hamiltonian-Type-Cycle-Neighbor}. Let m and n propose special {\tiny Hamiltonian-Type-Cycle-Neighbor}. Then with m4n,

\end{lemma}
Unknown environment 'proof'
Unknown environment 'theorem'
Unknown environment 'proof'

Unknown environment 'theorem'
Unknown environment 'proof'
Unknown environment 'proposition'
 Unknown environment 'proof'
 Unknown environment 'corollary'
 Unknown environment 'proof'
 Unknown environment 'theorem'
 Unknown environment 'proof'
Unknown environment 'definition'
 Unknown environment 'theorem'
 \begin{proof}
   Assume an Extreme SuperHyperGraph (NSHG) S is a pair S=(V,E). Consider S=(V,E) is a probability {\tiny Hamiltonian-Type-Cycle-Neighbor}. Let X be an Extreme Variable and let t be a positive real number. Then
 Math input error  

\end{proof}
Unknown environment 'corollary'
 Unknown environment 'proof'
Unknown environment 'theorem'
 Unknown environment 'proof'

Unknown environment 'corollary'
 Unknown environment 'proof'
Unknown environment 'definition'
Unknown environment 'definition'
 Unknown environment 'theorem'
 Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'

Unknown environment 'proposition'

Unknown environment 'proof'

\section{The Extreme Departures on The Theoretical Results Toward Theoretical Motivations}
The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses.
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
\section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation}
For the SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor},  Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, and the Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, some general results are introduced.
Unknown environment 'remark'
\begin{corollary}
 Assume Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. Then
 Extreme SuperHyperHamiltonianTypeCycleNeighbor={theSuperHyperHamiltonianTypeCycleNeighboroftheSuperHyperVertices | max|SuperHyperOffensiveSuperHyperHamiltonianTypeCycleNeighbor|ExtremecardinalityamidthoseSuperHyperHamiltonianTypeCycleNeighbor.}
plus one Extreme SuperHypeNeighbor to one. Where σi is the unary operation on the SuperHyperVertices of the SuperHyperGraph to assign the determinacy, the indeterminacy and the neutrality, for i=1,2,3, respectively.

\end{corollary}
Unknown environment 'corollary'
Unknown environment 'corollary'
Unknown environment 'corollary'
Unknown environment 'corollary'
Unknown environment 'corollary'
Unknown environment 'corollary'
Unknown environment 'corollary'
Unknown environment 'corollary'
Unknown environment 'corollary'
Unknown environment 'corollary'
Unknown environment 'corollary'

%

Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'

Unknown environment 'proposition'
Unknown environment 'proposition'

Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'

Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'

Unknown environment 'proposition'

Unknown environment 'proposition'

Unknown environment 'proposition'
Unknown environment 'proposition'
%
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'

Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'


Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'

Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'
Unknown environment 'proposition'

Unknown environment 'proposition'

            
 \section{Extreme Applications in Cancer's Extreme Recognition}
The cancer is the Extreme disease but the Extreme model is going to figure out what's going on this Extreme phenomenon. The special Extreme case of this Extreme disease is considered and as the consequences of the model, some parameters are used. The cells are under attack of this disease but the moves of the cancer in the special region are the matter of mind. The Extreme recognition of the cancer could help to find some Extreme treatments for this Extreme disease.
\
In the following, some Extreme steps are Extreme devised on this disease.
\begin{description}
 \item[Step 1. (Extreme Definition)] The Extreme recognition of the cancer in the long-term Extreme function.
  \item[Step 2. (Extreme Issue)] The specific region has been assigned by the Extreme model [it's called Extreme SuperHyperGraph] and the long Extreme cycle of the move from the cancer is identified by this research. Sometimes the move of the cancer hasn't be easily identified since there are some determinacy, indeterminacy and neutrality about the moves and the effects of the cancer on that region; this event leads us to choose another model [it's said to be Extreme SuperHyperGraph] to have convenient perception on what's happened and what's done.
 \item[Step 3. (Extreme Model)]  
There are some specific Extreme models, which are well-known and they've got the names, and some general Extreme models. The moves and the Extreme traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by an Extreme SuperHyperPath(-/SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,  SuperHyperWheel). The aim is to find either the Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} or the Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} in those Extreme Extreme SuperHyperModels.
  \section{Case 1: The Initial Extreme Steps Toward Extreme SuperHyperBipartite as  Extreme SuperHyperModel}

 \item[Step 4. (Extreme Solution)]
In the Extreme Figure (???), the Extreme SuperHyperBipartite is Extreme highlighted and Extreme featured.
Unknown environment 'figure'
\ By using the Extreme Figure (???) and the Table (???), the Extreme SuperHyperBipartite is obtained.
\
The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite ESHB:(V,E), in the Extreme SuperHyperModel (???),
is the Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}.
Unknown environment 'table'
    \section{Case 2: The Increasing Extreme Steps Toward Extreme SuperHyperMultipartite as Extreme SuperHyperModel}

     \item[Step 4. (Extreme Solution)]
In the Extreme Figure (???), the Extreme SuperHyperMultipartite is Extreme highlighted and  Extreme featured.
Unknown environment 'figure'
\
 By using the Extreme Figure (???) and the Table (???), the Extreme SuperHyperMultipartite is obtained.
 \
 The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite ESHM:(V,E), in the Extreme SuperHyperModel (???), is the  Extreme SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}.
Unknown environment 'table'
     \end{description}
\section{Wondering Open Problems But As The Directions To Forming The Motivations}
In what follows, some ``problems'' and some ``questions'' are proposed.
\
The   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and the Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} are defined on a real-world application, titled ``Cancer's Recognitions''.
Unknown environment 'question'
Unknown environment 'question'
Unknown environment 'question'
Unknown environment 'question'
Unknown environment 'problem'
Unknown environment 'problem'
Unknown environment 'problem'
\section{Conclusion and  Closing Remarks}
In this section, concluding remarks and closing remarks are represented. The drawbacks of this research are illustrated. Some benefits and some advantages of this research are highlighted.
\
This research uses some approaches to make Extreme SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. For that sake in the second definition, the main definition of the Extreme SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Extreme SuperHyperGraph, the new SuperHyperNotion, Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Extreme SuperHyperClasses are the cases of this research on the modeling of the regions where are under the attacks of the cancer to recognize this disease as it's mentioned on the title ``Cancer's Recognitions''. To formalize the instances on the SuperHyperNotion,   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor} and the Extreme   SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}. The clarifications, instances and literature reviews have taken the whole way through. In this research, the literature reviews have fulfilled the lines containing the notions and the results. The SuperHyperGraph and Extreme SuperHyperGraph are the SuperHyperModels on the ``Cancer's Recognitions'' and both bases are the background of this research. Sometimes the cancer has been happened on the region, full of cells, groups of cells and embedded styles. In this segment, the SuperHyperModel proposes some SuperHyperNotions based on the connectivities of the moves of the cancer in the longest and strongest styles with the formation of the design and the architecture are formally called ``  SuperHyper{\tiny Hamiltonian-Type-Cycle-Neighbor}'' in the themes of jargons and buzzwords. The prefix ``SuperHyper'' refers to the theme of the embedded styles to figure out the background for the SuperHyperNotions.
Unknown environment 'table'
In the Table (???), benefits and avenues for this research are, figured out, pointed out and spoken out.
      
      \section{
Extreme SuperHyperDuality But As The Extensions Excerpt From Dense And Super Forms}
Unknown environment 'definition'


Unknown environment 'definition'
\begin{example}\label{136EXM1}
 Assume an Extreme SuperHyperGraph (NSHG) S is a pair S=(V,E) in the mentioned Extreme Figures in every Extreme items.
 \begin{itemize}
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.  E1 and E3 are some empty Extreme  
 SuperHyperEdges but E2 is a loop Extreme SuperHyperEdge and E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality.
C(NSHG)Extreme SuperHyperDuality={E4}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperDuality={V4}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=3z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.  E1,E2 and E3 are some empty Extreme SuperHyperEdges but E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperDuality.
C(NSHG)Extreme SuperHyperDuality={E4}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperDuality={V4}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=3z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E4}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperDuality={V4}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=3z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E4,E2}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=2z2.C(NSHG)Extreme R-SuperHyperDuality={V1,V4}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=15z2.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E3}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=4z.C(NSHG)Extreme R-SuperHyperDuality={V5}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E3i+1i=03,E3i+24i=03}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial6z8.C(NSHG)Extreme R-SuperHyperDuality={V3i+1i=07}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=6z8.

 \item On the Figure (???),  the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E15,E16,E17}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperDuality={V3,V13,V8}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=4×5×5z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E4}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperDuality={V3,V13,V8}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=4×5×5z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E3i+1i=03,E23}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=3z5.C(NSHG)Extreme R-SuperHyperDuality={V3i+1i=03,V15}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=3z5.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E5}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperDuality={V3,V13,V8}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=4×5×5z3.

   \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E1,E3}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=z2.C(NSHG)Extreme R-SuperHyperDuality={V6,V1}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=3×3z2.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E1}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperDuality={V1,Vii=410i5,7,8}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=5z5.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E5,E9}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=z2.C(NSHG)Extreme R-SuperHyperDuality={V1,V6}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=3×3z2.

   \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E1}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=2z.C(NSHG)Extreme R-SuperHyperDuality={V1}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=z.

   \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E2,E5}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperDuality={V1,V4}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=z.

   \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E2,E5}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperDuality={V1,V4}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=(2×1×2)+(2×4×5)z.

   \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E2,E5}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperDuality={V1,V4}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=(1×1×2)z.

   \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E2,E5}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperDuality={V1,V4}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=(2×2×2)z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E3i+1i=03}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=3z4.C(NSHG)Extreme R-SuperHyperDuality={V2i+1i=05}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=2z6.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E6}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=10z.C(NSHG)Extreme R-SuperHyperDuality={V1}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E2}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=2z.C(NSHG)Extreme R-SuperHyperDuality={V1}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=10z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperDuality, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperDuality={E3,E4}.C(NSHG)Extreme SuperHyperDuality SuperHyperPolynomial=4z2.C(NSHG)Extreme R-SuperHyperDuality={V3,V6}.C(NSHG)Extreme R-SuperHyperDuality SuperHyperPolynomial=10×9+10×6+12×9+12×6z2.

\end{itemize}
\end{example}
The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses.
Unknown environment 'proposition'
Unknown environment 'proof'
\begin{example}\label{136EXM18a}
In the Figure (???), the connected Extreme SuperHyperPath ESHP:(V,E), is highlighted and featured. The Extreme SuperHyperSet,  in the Extreme SuperHyperModel (???), is the  SuperHyperDuality.

\end{example}

Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
\begin{proposition}
Assume a connected Extreme SuperHyperBipartite ESHB:(V,E). Then
C(NSHG)Extreme Quasi-SuperHyperDuality={EiEPiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme Quasi-SuperHyperDuality SuperHyperPolynomial=(i=|PESHG:(V,E)|(mini|PiESHG:(V,E)PESHG:(V,E)|)choose|PiESHG:(V,E)|)zmin|PiESHG:(V,E)PESHG:(V,E)|C(NSHG)Extreme Quasi-SuperHyperDuality={ViEXTERNALVPiESHG:(V,E)EXTERNAL,ViEXTERNALVPiESHG:(V,E)EXTERNAL, ij}.C(NSHG)Extreme Quasi-SuperHyperDuality SuperHyperPolynomial=|VESHG:(V,E)EXTERNAL|Extreme Cardinality=(i=|PESHG:(V,E)|(|PiESHG:(V,E)|choose 2)=z2.

\end{proposition}
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
            \section{
Extreme SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms}
Unknown environment 'definition'


Unknown environment 'definition'

\begin{example}\label{136EXM1}
 Assume an Extreme SuperHyperGraph (NSHG) S is a pair S=(V,E) in the mentioned Extreme Figures in every Extreme items.
 \begin{itemize}
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.  E1 and E3 are some empty Extreme  
 SuperHyperEdges but E2 is a loop Extreme SuperHyperEdge and E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin.
C(NSHG)Extreme SuperHyperJoin={E4}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperJoin={V1,V2,V4}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.  E1,E2 and E3 are some empty Extreme SuperHyperEdges but E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperJoin.
C(NSHG)Extreme SuperHyperJoin={E4}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperJoin={V1,V2,V4}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E4}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperJoin={V1,V2,V3}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E4,E2}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=2z2.C(NSHG)Extreme R-SuperHyperJoin={V1,V4}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=15z2.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E3}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=4z.C(NSHG)Extreme R-SuperHyperJoin={V5}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E3i+1i=03,E3i+24i=03}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial6z8.C(NSHG)Extreme R-SuperHyperJoin={V3i+1i=07}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=6z8.

 \item On the Figure (???),  the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E15,E16,E17}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperJoin={V3,V13,V8}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=4×5×5z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E4}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperJoin={V3,V13,V8}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=4×5×5z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E3i+1i=03,E23}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=3z5.C(NSHG)Extreme R-SuperHyperJoin={V3i+1i=03,V15}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=3z5.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E5}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperJoin={V3,V13,V8}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=4×5×5z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E1,E3}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=z2.C(NSHG)Extreme R-SuperHyperJoin={V6,V1}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=3×3z2.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E1}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperJoin={V1,Vii=410i5,7,8}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=5z5.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E3,E9}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=z2.C(NSHG)Extreme R-SuperHyperJoin={V1,V6}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=3×3z2.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E1}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=2z.C(NSHG)Extreme R-SuperHyperJoin={V1}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E2,E5}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperJoin={V1,V4}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E2,E5}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperJoin={V2,V7,V17}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=(1×5×5)+(1×2+1)z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E2,E5}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperJoin={V27,V2,V7,V17}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=(1×1×2+1)z4.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E2,E5}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperJoin={V27,V2,V7,V17}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=(1×1×2+1)z4.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E3i+1i=03}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=3z4.C(NSHG)Extreme R-SuperHyperJoin={V2i+1i=05}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=2z6.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E6}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=10z.C(NSHG)Extreme R-SuperHyperJoin={V1}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E2}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=2z.C(NSHG)Extreme R-SuperHyperJoin={V1}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=10z.
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperJoin, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperJoin={E2,E4}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperJoin={V3,V6}.C(NSHG)Extreme R-SuperHyperJoin SuperHyperPolynomial=10×6+10×6+12×6+12×6z2.
\end{itemize}
\end{example}
The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses.
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'

Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
\begin{proposition}
Assume a connected Extreme SuperHyperBipartite ESHB:(V,E). Then
C(NSHG)Extreme Quasi-SuperHyperJoin=(PERFECT MATCHING).{EiEPiESHG:(V,E), PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme Quasi-SuperHyperJoin=(OTHERWISE).{},If PiESHG:(V,E), |PiESHG:(V,E)|mini|PiESHG:(V,E)PESHG:(V,E)|.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=(PERFECT MATCHING).=(i=|PESHG:(V,E)|(mini|PiESHG:(V,E)PESHG:(V,E)|)choose|PiESHG:(V,E)|)zmin|PiESHG:(V,E)PESHG:(V,E)|where PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme SuperHyperJoin SuperHyperPolynomial=(OTHERWISE)0.C(NSHG)Extreme Quasi-SuperHyperJoin={ViEXTERNALVPiESHG:(V,E)EXTERNAL,ViEXTERNALVPiESHG:(V,E)EXTERNAL, ij}.C(NSHG)Extreme Quasi-SuperHyperJoin SuperHyperPolynomial=|VESHG:(V,E)EXTERNAL|Extreme Cardinality=(i=|PESHG:(V,E)|(|PiESHG:(V,E)|choose 2)=z2.

\end{proposition}
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
\begin{example}\label{136EXM23a}
In the Extreme Figure (???), the connected Extreme SuperHyperWheel NSHW:(V,E), is Extreme highlighted and featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperWheel ESHW:(V,E),
in the Extreme SuperHyperModel (???), is the  Extreme SuperHyperJoin.

            \end{example}
           \section{
Extreme SuperHyperPerfect But As The Extensions Excerpt From Dense And Super Forms}
Unknown environment 'definition'


Unknown environment 'definition'

\begin{example}\label{136EXM1}
 Assume an Extreme SuperHyperGraph (NSHG) S is a pair S=(V,E) in the mentioned Extreme Figures in every Extreme items.
 \begin{itemize}
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.  E1 and E3 are some empty Extreme  
 SuperHyperEdges but E2 is a loop Extreme SuperHyperEdge and E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect.
C(NSHG)Extreme SuperHyperPerfect={E4}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperPerfect={V4}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=3z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.  E1,E2 and E3 are some empty Extreme SuperHyperEdges but E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperPerfect.
C(NSHG)Extreme SuperHyperPerfect={E4}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperPerfect={V4}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=3z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E4}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperPerfect={V4}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=3z.
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E4,E2}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=2z2.C(NSHG)Extreme R-SuperHyperPerfect={V1,V4}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=15z2.
  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E3}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=4z.C(NSHG)Extreme R-SuperHyperPerfect={V5}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E3i+1i=03,E3i+24i=03}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial6z8.C(NSHG)Extreme R-SuperHyperPerfect={V3i+1i=07}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=6z8.

 \item On the Figure (???),  the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E15,E16,E17}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperPerfect={V3,V6,V8}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=3×4×4z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E4}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperPerfect={V3,V6,V8}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=3×4×4z3.
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperPerfect={E3i+1i=03,E23}.C(NSHG)Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial=3z5.C(NSHG)Extreme R-Quasi-SuperHyperPerfect={V3i+1i=03,V15}.C(NSHG)Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial=3z5.
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E5}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperPerfect={V3,V6,V8}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=3×4×4z3.
  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E1,E3}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z2.C(NSHG)Extreme R-SuperHyperPerfect={V6,V1}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=3×2z2.
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E1}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperPerfect={V1,Vii=410i5,7,8}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=5z5.
  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E3,E9}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z2.C(NSHG)Extreme R-SuperHyperPerfect={V1,V6}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=3×3z2.
  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E1}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=2z.C(NSHG)Extreme R-SuperHyperPerfect={V1}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E2,E5}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=3z2.C(NSHG)Extreme R-SuperHyperPerfect={V1,V4}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=z.
  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E2,E5}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=3z2.C(NSHG)Extreme R-Quasi-SuperHyperPerfect={V2,V7,V17}.C(NSHG)Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial=(1×5×5)+(1×2+1)z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E2,E5}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=3z2.C(NSHG)Extreme R-Quasi-SuperHyperPerfect={V27,V2,V7,V17}.C(NSHG)Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial=(1×1×2+1)z4.
  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E2,E5}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=3z2.C(NSHG)Extreme R-Quasi-SuperHyperPerfect={V27,V2,V7,V17}.C(NSHG)Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial=(1×1×2+1)z4.
  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E3i+1i=03}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=3z4.C(NSHG)Extreme R-Quasi-SuperHyperPerfect={V2i+1i=05}.C(NSHG)Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial=2z6.
  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E6}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=10z.C(NSHG)Extreme R-SuperHyperPerfect={V1}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=z.
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E2}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=2z.C(NSHG)Extreme R-SuperHyperPerfect={V1}.C(NSHG)Extreme R-SuperHyperPerfect SuperHyperPolynomial=10z.
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperPerfect, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperPerfect={E2,E5}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=z2.C(NSHG)Extreme R-Quasi-SuperHyperPerfect={V3,V6}.C(NSHG)Extreme R-Quasi-SuperHyperPerfect SuperHyperPolynomial=10×6+10×6+12×6+12×6z2.
\end{itemize}
\end{example}
The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses.
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'

Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
\begin{proposition}
Assume a connected Extreme SuperHyperBipartite ESHB:(V,E). Then
C(NSHG)Extreme Quasi-SuperHyperPerfect=(PERFECT MATCHING).{EiEPiESHG:(V,E), PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme Quasi-SuperHyperPerfect=(OTHERWISE).{},If PiESHG:(V,E), |PiESHG:(V,E)|mini|PiESHG:(V,E)PESHG:(V,E)|.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=(PERFECT MATCHING).=(i=|PESHG:(V,E)|(mini|PiESHG:(V,E)PESHG:(V,E)|)choose|PiESHG:(V,E)|)zmin|PiESHG:(V,E)PESHG:(V,E)|where PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme SuperHyperPerfect SuperHyperPolynomial=(OTHERWISE)0.C(NSHG)Extreme Quasi-SuperHyperPerfect={ViEXTERNALVPiESHG:(V,E)EXTERNAL,ViEXTERNALVPiESHG:(V,E)EXTERNAL, ij}.C(NSHG)Extreme Quasi-SuperHyperPerfect SuperHyperPolynomial=|VESHG:(V,E)EXTERNAL|Extreme Cardinality=(i=|PESHG:(V,E)|(|PiESHG:(V,E)|choose 2)=z2.

\end{proposition}
Unknown environment 'proof'
\begin{example}\label{136EXM21a}
In the Extreme Figure (???), the connected Extreme SuperHyperBipartite ESHB:(V,E), is Extreme highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Extreme Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperBipartite ESHB:(V,E), in the Extreme SuperHyperModel (???), is the Extreme  SuperHyperPerfect.

\end{example}
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'

\section{
Extreme SuperHyperTotal But As The Extensions Excerpt From Dense And Super Forms}
Unknown environment 'definition'


Unknown environment 'definition'

\begin{example}\label{136EXM1}
 Assume an Extreme SuperHyperGraph (NSHG) S is a pair S=(V,E) in the mentioned Extreme Figures in every Extreme items.
 \begin{itemize}
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.  E1 and E3 are some empty Extreme  
 SuperHyperEdges but E2 is a loop Extreme SuperHyperEdge and E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal.
C(NSHG)Extreme Quasi-SuperHyperTotal={E4}.C(NSHG)Extreme Quasi-SuperHyperTotal SuperHyperPolynomial=z.C(NSHG)Extreme R-Quasi-SuperHyperTotal={V4}.C(NSHG)Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial=3z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.  E1,E2 and E3 are some empty Extreme SuperHyperEdges but E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperTotal.
C(NSHG)Extreme Quasi-SuperHyperTotal={E4}.C(NSHG)Extreme Quasi-SuperHyperTotal SuperHyperPolynomial=z.C(NSHG)Extreme R-Quasi-SuperHyperTotal={V4}.C(NSHG)Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial=3z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperTotal={E4}.C(NSHG)Extreme Quasi-SuperHyperTotal SuperHyperPolynomial=z.C(NSHG)Extreme R-Quasi-SuperHyperTotal={V4}.C(NSHG)Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial=3z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-={E4,E2}.C(NSHG)Extreme Quasi-SuperHyperTotal SuperHyperPolynomial=2z2.C(NSHG)Extreme R-Quasi-SuperHyperTotal={V1,V4}.C(NSHG)Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial=15z2.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperTotal={E3}.C(NSHG)Extreme Quasi-SuperHyperTotal SuperHyperPolynomial=4z.C(NSHG)Extreme R-Quasi-SuperHyperTotal={V5}.C(NSHG)Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={Ei+1i=09}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial20z10.C(NSHG)Extreme R-SuperHyperTotal={Vi+1i=09}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=20z10.

 \item On the Figure (???),  the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E12,E13,E14}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperTotal={V12,V13,V14}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperTotal={E4}.C(NSHG)Extreme Quasi-SuperHyperTotal SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperTotal={V12,V13,V14}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=3×4×4z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={Ei+1i=09}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial10z10.C(NSHG)Extreme R-SuperHyperTotal={Vi+1i=09}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=20z10.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperTotal={E5}.C(NSHG)Extreme Quasi-SuperHyperTotal SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperTotal={V12,V13,V14}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=3×4×4z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E1,E6,E7,E8}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=2z4.C(NSHG)Extreme R-SuperHyperTotal={V1,V5}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=3z2.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E1,E2}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=5z2.C(NSHG)Extreme R-SuperHyperTotal={V1,Vii=18i4,5,6}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=z5.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E3,E9,E6}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=3z3.C(NSHG)Extreme R-SuperHyperTotal={V1,V5}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=3z2.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E1,E2}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=z2.C(NSHG)Extreme R-SuperHyperTotal={V1,V3}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=2z2.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E2,E3,E4}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperTotal={V2,V3,V4}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E2,E3,E4}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperTotal={V2,V6,V17}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=4×3z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E2,E3,E4}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperTotal={V1,V2,V6,V17}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=4×3z4.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E2,E3,E4}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperTotal={V1,V2,V6,V17}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=2×4×3z4.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={Ei+2i=011}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=11z10.C(NSHG)Extreme R-Quasi-SuperHyperTotal={Vi+2i=011}.C(NSHG)Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial=11z10.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E6,E10}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=9z2.C(NSHG)Extreme R-SuperHyperTotal={V1,V}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=|(|V|1)z2.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E1,E2}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=2z2.C(NSHG)Extreme R-SuperHyperTotal={V1,V2}.C(NSHG)Extreme R-SuperHyperTotal SuperHyperPolynomial=9z2.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperTotal, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperTotal={E3,E4}.C(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=z2.C(NSHG)Extreme R-Quasi-SuperHyperTotal={V3,V10,V6}.C(NSHG)Extreme R-Quasi-SuperHyperTotal SuperHyperPolynomial=3×6z3.

\end{itemize}
\end{example}
The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses.
Unknown environment 'proposition'
Unknown environment 'proof'
\begin{example}\label{136EXM18a}
In the Figure (???), the connected Extreme SuperHyperPath ESHP:(V,E), is highlighted and featured. The Extreme SuperHyperSet,  in the Extreme SuperHyperModel (???), is the  SuperHyperTotal.

\end{example}

\begin{proposition}
Assume a connected Extreme SuperHyperCycle ESHC:(V,E). Then
\begin{eqnarray*}
 &&
          \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal}}=
         \&&=\{E_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}.
 \&&
 \mathcal{C}(NSHG)_{\text{Extreme SuperHyperTotal SuperHyperPolynomial}}
 \&&=({|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-1)
  \&&
 z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}.
 \&&
   \mathcal{C}(NSHG)_{\text{Extreme R-SuperHyperTotal}}
    \&&=\{V^{EXTERNAL}_i\}_{i=1}^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}.
\&&
  \mathcal{C}(NSHG)_{{\small\text{Extreme R-SuperHyperTotal SuperHyperPolynomial}}}
  \&&
=\prod |{V^{EXTERNAL}}_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}
z^{|E_{ESHG:(V,E)}|_{\text{Extreme Cardinality}}-2}
\end{eqnarray*}
\end{proposition}
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
\begin{proposition}
Assume a connected Extreme SuperHyperBipartite ESHB:(V,E). Then
C(NSHG)Extreme SuperHyperTotal={EaEPiESHG:(V,E), PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme SuperHyperTotalC(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=zmin|PiESHG:(V,E)PESHG:(V,E)|where PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme SuperHyperTotal={VaEXTERNALVPiESHG:(V,E)EXTERNAL,VbEXTERNALVPiESHG:(V,E)EXTERNAL, ij}.C(NSHG)Extreme Quasi-SuperHyperTotal SuperHyperPolynomial=|VESHG:(V,E)EXTERNAL|Extreme Cardinality=(i=|PESHG:(V,E)|(|PiESHG:(V,E)|choose 2)=z2.

\end{proposition}
Unknown environment 'proof'
Unknown environment 'example'
\begin{proposition}
Assume a connected Extreme SuperHyperMultipartite ESHM:(V,E). Then
C(NSHG)Extreme SuperHyperTotal={EaEPiESHG:(V,E), PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme SuperHyperTotalC(NSHG)Extreme SuperHyperTotal SuperHyperPolynomial=zmin|PiESHG:(V,E)PESHG:(V,E)|where PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme SuperHyperTotal={VaEXTERNALVPiESHG:(V,E)EXTERNAL,VbEXTERNALVPiESHG:(V,E)EXTERNAL, ij}.C(NSHG)Extreme Quasi-SuperHyperTotal SuperHyperPolynomial=|VESHG:(V,E)EXTERNAL|Extreme Cardinality=(i=|PESHG:(V,E)|(|PiESHG:(V,E)|choose 2)=z2.

\end{proposition}
Unknown environment 'proof'
\begin{example}\label{136EXM22a}
In the Figure (???), the connected Extreme SuperHyperMultipartite ESHM:(V,E), is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite ESHM:(V,E), in the Extreme SuperHyperModel (???), is the  Extreme SuperHyperTotal.

\end{example}
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
    \section{
Extreme SuperHyperConnected But As The Extensions Excerpt From Dense And Super Forms}        
            
Unknown environment 'definition'


Unknown environment 'definition'

\begin{example}\label{136EXM1}
 Assume an Extreme SuperHyperGraph (NSHG) S is a pair S=(V,E) in the mentioned Extreme Figures in every Extreme items.
 \begin{itemize}
 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.  E1 and E3 are some empty Extreme  
 SuperHyperEdges but E2 is a loop Extreme SuperHyperEdge and E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected.
C(NSHG)Extreme SuperHyperConnected={E4}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperConnected={V4}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=3z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.  E1,E2 and E3 are some empty Extreme SuperHyperEdges but E4 is an Extreme SuperHyperEdge. Thus in the terms of Extreme SuperHyperNeighbor, there's only one Extreme SuperHyperEdge, namely, E4. The Extreme SuperHyperVertex, V3 is Extreme isolated means that there's no Extreme SuperHyperEdge has it as an Extreme endpoint. Thus the Extreme SuperHyperVertex, V3,  \underline{\textbf{is}} excluded in every given Extreme SuperHyperConnected.
C(NSHG)Extreme SuperHyperConnected={E4}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperConnected={V4}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=3z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E4}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperConnected={V4}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=3z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E1,E2,E4}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=z3.C(NSHG)Extreme R-Quasi-SuperHyperConnected={V1,V4}.C(NSHG)Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial=15z2.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E3}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=4z.C(NSHG)Extreme R-SuperHyperConnected={V5}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={Ei+1i=09}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial20z10.C(NSHG)Extreme R-Quasi-SuperHyperConnected={Vi+1i=09}.C(NSHG)Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial=20z10.

 \item On the Figure (???),  the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E12,E13,E14}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperConnected={V12,V13,V14}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={E4}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperConnected={V12,V13,V14}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=3×4×4z3.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={Ei+1i=09}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial10z10.C(NSHG)Extreme R-SuperHyperConnected={Vi+1i=1119,V22}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=20z10.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E5}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperConnected={V12,V13,V14}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=3×4×4z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={E1,E6,E7,E8}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=2z4.C(NSHG)Extreme R-Quasi-SuperHyperConnected={V1,V5}.C(NSHG)Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial=3z2.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E1,E2}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=5z2.C(NSHG)Extreme R-Quasi-SuperHyperConnected={V1,Vii=18i4,5,6}.C(NSHG)Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial=z5.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={E3,E9,E6}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=3z3.C(NSHG)Extreme R-SuperHyperConnected={V1,V5}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=3z2.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E2}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperConnected={V1}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=z.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={E2,E3,E4}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=z3.C(NSHG)Extreme R-Quasi-SuperHyperConnected={V2,V3,V4}.C(NSHG)Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial=z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E2,E3,E4}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=z3.C(NSHG)Extreme R-SuperHyperConnected={V2,V6,V17}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=4×3z3.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={E2,E3,E4}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=z3.C(NSHG)Extreme R-Quasi-SuperHyperConnected={V1,V2,V6,V17}.C(NSHG)Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial=4×3z4.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={E2,E3,E4}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=z3.C(NSHG)Extreme R-Quasi-SuperHyperConnected={V1,V2,V6,V17}.C(NSHG)Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial=2×4×3z4.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={Ei+2i=011}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=11z10.C(NSHG)Extreme R-Quasi-SuperHyperConnected={Vi+2i=011}.C(NSHG)Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial=11z10.

  \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E6}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=10z.C(NSHG)Extreme R-SuperHyperConnected={V1}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme SuperHyperConnected={E2}.C(NSHG)Extreme SuperHyperConnected SuperHyperPolynomial=z.C(NSHG)Extreme R-SuperHyperConnected={V1}.C(NSHG)Extreme R-SuperHyperConnected SuperHyperPolynomial=10z.

 \item On the Figure (???), the Extreme SuperHyperNotion, namely, Extreme SuperHyperConnected, is up. The Extreme Algorithm is Extremely straightforward.
C(NSHG)Extreme Quasi-SuperHyperConnected={E3,E4}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=z2.C(NSHG)Extreme R-Quasi-SuperHyperConnected={V3,V10,V6}.C(NSHG)Extreme R-Quasi-SuperHyperConnected SuperHyperPolynomial=3×6z3.

\end{itemize}
\end{example}
The previous Extreme approach apply on the upcoming Extreme results on Extreme SuperHyperClasses.
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'

Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
\begin{proposition}
Assume a connected Extreme SuperHyperBipartite ESHB:(V,E). Then
C(NSHG)Extreme Quasi-SuperHyperConnected={EaEPiESHG:(V,E), PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=zmin|PiESHG:(V,E)PESHG:(V,E)|where PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme V-SuperHyperConnected={VaEXTERNALVPiESHG:(V,E)EXTERNAL,VbEXTERNALVPiESHG:(V,E)EXTERNAL, ij}.C(NSHG)Extreme V-SuperHyperConnected SuperHyperPolynomial=|VESHG:(V,E)EXTERNAL|Extreme Cardinality=(i=|PESHG:(V,E)|(|PiESHG:(V,E)|choose 2)=z2.

\end{proposition}
Unknown environment 'proof'
Unknown environment 'example'
\begin{proposition}
Assume a connected Extreme SuperHyperMultipartite ESHM:(V,E). Then
C(NSHG)Extreme Quasi-SuperHyperConnected={EaEPiESHG:(V,E), PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme Quasi-SuperHyperConnected SuperHyperPolynomial=zmin|PiESHG:(V,E)PESHG:(V,E)|where PiESHG:(V,E), |PiESHG:(V,E)|=mini|PiESHG:(V,E)PESHG:(V,E)|}.C(NSHG)Extreme V-SuperHyperConnected={VaEXTERNALVPiESHG:(V,E)EXTERNAL,VbEXTERNALVPiESHG:(V,E)EXTERNAL, ij}.C(NSHG)Extreme V-SuperHyperConnected SuperHyperPolynomial=|VESHG:(V,E)EXTERNAL|Extreme Cardinality=(i=|PESHG:(V,E)|(|PiESHG:(V,E)|choose 2)=z2.

\end{proposition}
Unknown environment 'proof'
\begin{example}\label{136EXM22a}
In the Figure (???), the connected Extreme SuperHyperMultipartite ESHM:(V,E), is highlighted and Extreme featured. The obtained Extreme SuperHyperSet, by the Algorithm in previous Extreme result, of the Extreme SuperHyperVertices of the connected Extreme SuperHyperMultipartite ESHM:(V,E), in the Extreme SuperHyperModel (???), is the  Extreme SuperHyperConnected.

\end{example}
Unknown environment 'proposition'
Unknown environment 'proof'
Unknown environment 'example'
\section{Background}
There are some scientific researches covering the topic of this research. In what follows, there are some discussion and literature reviews about them.
\
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{HG1} 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 ISO 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{HG2} 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 ISO 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.
\
The seminal paper and groundbreaking article is titled ``Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer’s Treatments'' in \textbf{Ref.} \cite{HG3} by Henry Garrett (2023). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental notions and using vital tools in Cancer’s Treatments. It's published in prestigious and fancy journal is entitled “Journal of Mathematical Techniques and Computational Mathematics(JMTCM)” with ISO abbreviation ``J Math Techniques Comput Math'' in volume 2 and issue 1 with pages 35-47. 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), and \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,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184,HG185,HG186,HG187,HG188,HG189,HG190,HG191,HG192,HG193,HG194,HG195,HG196,HG197,HG198,HG199,HG200,HG201,HG202,HG203,HG204,HG205,HG206,HG207,HG208,HG209,HG210,HG211,HG212,HG213,HG214,HG215,HG216,HG217,HG218,HG219,HG220,HG221,HG222,HG223,HG224,HG225,HG226,HG228,HG230,HG231,HG232,HG233,HG234,HG236}, there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph alongside scientific research books at \cite{HG60b,HG61b,HG62b,HG63b,HG64b,HG65b,HG66b,HG67b,HG68b,HG69b,HG70b,HG71b,HG72b,HG73b,HG74b,HG75b,HG76b,HG77b,HG78b,HG79b,HG80b,HG81b,HG82b,HG83b,HG84b,HG85b,HG86b,HG87b,HG88b,HG89b,HG90b,HG91b,HG92b,HG93b,HG94b,HG95b,HG96b,HG97b,HG98b,HG99b,HG100b,HG101b,HG102b,HG103b,HG104b,HG105b,HG106b,HG107b,HG108b,HG109b,HG110b,HG111b,HG112b,HG113b,HG114b,HG115b,HG116b,HG117b,HG118b,HG119b,HG120b,HG121b,HG122b,HG123b,HG124b,HG125b,HG126b,HG127b,HG128b,HG129b,HG130b,HG131b,HG132b,HG133b,HG134b,HG135b,HG136b,HG137b,HG138b,HG139b,HG140b,HG141b,HG142b,HG143b,HG144b,HG145b,HG146b,HG147b,HG148b,HG149b,HG150b,HG151b,HG152b,HG153b,HG154b,HG155b}. Two popular scientific research books in Scribd in the terms of high readers, 4190 and 5189 respectively,  on neutrosophic science is on \cite{HG32b,HG44b}.  
\
Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG71b} by Henry Garrett (2023) which is indexed by Google Scholar and has more than 4216 readers in Scribd. It's titled ``Beyond Neutrosophic Graphs'' and published by Dr. Henry Garrett. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory.
\
Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG70b} by Henry Garrett (2023) which is indexed by Google Scholar and has more than 5214 readers in Scribd. It's titled ``Neutrosophic Duality'' and published by Dr. Henry Garrett. 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 scientific researches \cite{HG1,HG2,HG3}. The formalization of the notions on the framework of notions in SuperHyperGraphs, Neutrosophic notions in SuperHyperGraphs 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,HG94,HG942,HG95,HG952,HG96,HG962,HG97,HG972,HG98,HG982,HG106,HG107,HG111,HG112,HG115,HG116,HG120,HG121,HG122,HG123,HG124,HG125,HG126,HG127,HG128,HG129,HG130,HG131,HG132,HG134,HG135,HG136,HG137,HG138,HG139,HG140,HG141,HG142,HG143,HG144,HG145,HG146,HG147,HG148,HG149,HG150,HG151,HG152,HG153,HG154,HG155,HG156,HG157,HG158,HG159,HG160,HG161,HG162,HG163,HG164,HG165,HG166,HG167,HG168,HG169,HG170,HG171,HG172,HG173,HG174,HG175,HG176,HG177,HG178,HG179,HG180,HG181,HG182,HG183,HG184,HG185,HG186,HG187,HG188,HG189,HG190,HG191,HG192,HG193,HG194,HG195,HG196,HG197,HG198,HG199,HG200,HG201,HG202,HG203,HG204,HG205,HG206,HG207,HG208,HG209,HG210,HG211,HG212,HG213,HG214,HG215,HG216,HG217,HG218,HG219,HG220,HG221,HG222,HG223,HG224,HG225,HG226,HG228,HG230,HG231,HG232,HG233,HG234,HG236} alongside scientific research books at \cite{HG60b,HG61b,HG62b,HG63b,HG64b,HG65b,HG66b,HG67b,HG68b,HG69b,HG70b,HG71b,HG72b,HG73b,HG74b,HG75b,HG76b,HG77b,HG78b,HG79b,HG80b,HG81b,HG82b,HG83b,HG84b,HG85b,HG86b,HG87b,HG88b,HG89b,HG90b,HG91b,HG92b,HG93b,HG94b,HG95b,HG96b,HG97b,HG98b,HG99b,HG100b,HG101b,HG102b,HG103b,HG104b,HG105b,HG106b,HG107b,HG108b,HG109b,HG110b,HG111b,HG112b,HG113b,HG114b,HG115b,HG116b,HG117b,HG118b,HG119b,HG120b,HG121b,HG122b,HG123b,HG124b,HG125b,HG126b,HG127b,HG128b,HG129b,HG130b,HG131b,HG132b,HG133b,HG134b,HG135b,HG136b,HG137b,HG138b,HG139b,HG140b,HG141b,HG142b,HG143b,HG144b,HG145b,HG146b,HG147b,HG148b,HG149b,HG150b,HG151b,HG152b,HG153b,HG154b,HG155b}. Two popular scientific research books in Scribd in the terms of high readers, 4216 and 5214 respectively,  on neutrosophic science is on \cite{HG32b,HG44b}.


\begin{thebibliography}{595}

\bibitem{HG1} 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{HG2} Henry Garrett, “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. (doi: 10.33140/JMTCM.01.03.09)

\bibitem{HG3} Henry Garrett, “Some Super Hyper Degrees and Co-Super Hyper Degrees on Neutrosophic Super Hyper Graphs And Super Hyper Graphs Alongside Applications in Cancer’s Treatments”, J Math Techniques Comput Math 2(1) (2023) 35-47. (https://www.opastpublishers.com/open-access-articles/some-super-hyper-degrees-and-cosuper-hyper-degrees-on-neutrosophic-super-hyper-graphs-and-super-hyper-graphs-alongside-a.pdf)

\bibitem{HG216} Henry Garrett, “A Research on Cancers Recognition and Neutrosophic Super Hypergraph by Eulerian Super Hyper Cycles and Hamiltonian Sets as Hyper Covering Versus Super separations”, J Math Techniques Comput Math 2(3) (2023) 136-148. (https://www.opastpublishers.com/open-access-articles/a-research-on-cancers-recognition-and-neutrosophic-super-hypergraph-by-eulerian-super-hyper-cycles-and-hamiltonian-sets-.pdf)

\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{HG236}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Type-Cycle-Neighbor As Hyper Nebbish On Super Nebulous”, Zenodo 2023, (doi: 10.5281/zenodo.7806767).
\bibitem{HG234}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Type-Cycle-Decomposition As Hyper Decompress On Super Decompensation”, Zenodo 2023, (doi: 10.5281/zenodo.7804238).
\bibitem{HG233}
Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Hamiltonian-Type-Cycle-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7804228).
\bibitem{HG232}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Type-Cycle-Cut As Hyper Hamper On Super Hammy”, Zenodo 2023, (doi: 10.5281/zenodo.7799902).
\bibitem{HG231}
Henry Garrett, “New Ideas On Super Hammy By Hyper Hamper Of Hamiltonian-Type-Cycle-Cut In Recognition of Cancer With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7804218).
\bibitem{HG230}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Cycle-Neighbor As Hyper Nebbish On Super Nebulous”, Zenodo 2023, (doi: 10.5281/zenodo.7796334).
\bibitem{HG228}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Cycle-Decomposition As Hyper Decompress On Super Decompensation”, Zenodo 2023, (doi: 10.5281/zenodo.7793372).
\bibitem{HG226}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Cycle-Cut As Hyper Hamper On Super Hammy”, Zenodo 2023, (doi: 10.5281/zenodo.7791952).
\bibitem{HG225}
Henry Garrett, “New Ideas On Super Hammy By Hyper Hamper Of Hamiltonian-Cycle-Cut In Recognition of Cancer With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7791982).
\bibitem{HG224}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Neighbor As Hyper Nebbish On Super Nebulous”, Zenodo 2023, (doi: 10.5281/zenodo.7790026).
\bibitem{HG223}
Henry Garrett, “New Ideas On Super Nebulous By Hyper Nebbish Of Hamiltonian-Neighbor In Recognition of Cancer With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7790052).
\bibitem{HG222}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Decomposition As Hyper Decompress On Super Decompensation”, Zenodo 2023, (doi: 10.5281/zenodo.7787066).
\bibitem{HG221}
Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Hamiltonian-Decomposition In Recognition of Cancer With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7787094).
\bibitem{HG220}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Hamiltonian-Cut As Hyper Hamper On Super Hammy”, Zenodo 2023, (doi: 10.5281/zenodo.7781476).
\bibitem{HG219}
Henry Garrett, “New Ideas On Super Hammy By Hyper Hamper Of Hamiltonian-Cut In Recognition of Cancer With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7783082).
\bibitem{HG218}
Henry Garrett, “New Ideas In Recognition of Cancer And Neutrosophic SuperHyperGraph By Trace-Neighbor As Hyper Nebbish On Super Nebulous”, Zenodo 2023, (doi: 10.5281/zenodo.7777857).
\bibitem{HG217}
Henry Garrett, “New Ideas On Super Nebulous By Hyper Nebbish Of Trace-Neighbor In Recognition of Cancer With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7779286).
\bibitem{HG215}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Trace-Decomposition As Hyper Decompress On Super Decompensation”, Zenodo 2023, (doi: 10.5281/zenodo.7771831).
\bibitem{HG214}
Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Trace-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7772468).
\bibitem{HG213}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Trace-Cut As Hyper Nebbish On Super Nebulous”, ResearchGate 2023, (doi: 10.13140/RG.2.2.20913.25446).
\bibitem{HG212}
Henry Garrett, “New Ideas On Super Tract By Hyper Track Of Trace-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, Zenodo 2023, (doi: 10.5281/zenodo.7764916).
\bibitem{HG211}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Edge-Neighbor As Hyper Nebbish On Super Nebulous”, ResearchGate 2023, (doi: 10.13140/RG.2.2.11770.98247).
\bibitem{HG210}
Henry Garrett, “New Ideas On Super Nebulous By Hyper Nebbish Of Edge-Neighbor In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.12400.12808).
\bibitem{HG209}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Edge-Decomposition As Hyper Decompress On Super Decompensation”, ResearchGate 2023, (doi: 10.13140/RG.2.2.22545.10089).
\bibitem{HG208}
Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Edge-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.29544.34564).
\bibitem{HG207}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Edge-Cut As Hyper Edify On Super Eddy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.11377.76644).
\bibitem{HG206}
Henry Garrett, “New Ideas On Super Eddy By Hyper Edify Of Edge-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23750.96329).
\bibitem{HG205}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Neighbor As Hyper Nebbish On Super Nebulous”, ResearchGate 2023, (doi: 10.13140/RG.2.2.31366.24641).
\bibitem{HG204}
Henry Garrett, “New Ideas On Super Nebulous By Hyper Nebbish Of Vertex-Neighbor In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.34721.68960).
\bibitem{HG203}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Decomposition As Hyper Decompress On Super Decompensation”, ResearchGate 2023, (doi: 10.13140/RG.2.2.30212.81289).
\bibitem{HG202}
Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Vertex-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.18468.76169).
\bibitem{HG201}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Cut As Hyper Vertu On Super Vertigo”, ResearchGate 2023, (doi: 10.13140/RG.2.2.24288.35842).
\bibitem{HG200}
Henry Garrett, “New Ideas On Super Vertigo By Hyper Vertu Of Vertex-Cut In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.32467.25124).
\bibitem{HG199}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Stable-Neighbor As Hyper Nebbish On Super Nebulous”, ResearchGate 2023, (doi: 10.13140/RG.2.2.31025.45925).
\bibitem{HG198}
Henry Garrett, “New Ideas On Super Nebulizer By Hyper Nub Of Stable-Neighbor In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.17184.25602).
\bibitem{HG197}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Stable-Decompositions As Hyper Stain On Super Stagy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23423.28327).
\bibitem{HG196}
Henry Garrett, “New Ideas On Super Stale By Hyper Stalk Of Stable-Decompositions In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.28456.44805).
\bibitem{HG195}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By
Stable-Cut As Hyper Stain On Super Stagy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23525.68320).
\bibitem{HG194}
Henry Garrett, “New Ideas On Super Stale By Hyper Stalk Of Stable-Cut In Cancer's Recognition
With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.20170.24000).
\bibitem{HG193}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By
Clique-Neighbors As Hyper Nebbish On Super Nebulous”, ResearchGate 2023, (doi:  10.13140/RG.2.2.36475.59683).
\bibitem{HG192}
Henry Garrett, “New Ideas On Super Nebulizer By Hyper Nub Of Clique-Neighbors In Cancer's
Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi:  10.13140/RG.2.2.29764.71046).
\bibitem{HG191}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By
Clique-Decompositions As Hyper Decompile On Super Decommission”, ResearchGate 2023, (doi:  10.13140/RG.2.2.18780.87683).
\bibitem{HG190}
Henry Garrett, “New Ideas On Super Decompensation By Hyper Decompress Of Clique-
Decompositions In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.27169.48487).
\bibitem{HG189}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By
Clique-Cut As Hyper Click On Super Cliche”, ResearchGate 2023, (doi: 10.13140/RG.2.2.26134.01603).
\bibitem{HG188}
Henry Garrett, “New Ideas On Super Cliff By Hyper Cling Of Clique-Cut In Cancer's Recognition
With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.27392.30721).
\bibitem{HG187}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By
Space As Hyper Spin On Super Spacy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.33028.40321).
\bibitem{HG186}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By List-
Coloring As Hyper List On Super Lisle”, ResearchGate 2023, (doi: 10.13140/RG.2.2.21389.20966).
\bibitem{HG185}
Henry Garrett, “New Ideas On Super Lith By Hyper Lite Of List-Coloring In Cancer's Recognition
With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.16356.04489).
\bibitem{HG184}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Space As Hyper Sparse On Super Spark”, ResearchGate 2023, (doi: 10.13140/RG.2.2.21756.21129).
\bibitem{HG183}
Henry Garrett, “New Ideas On Super Solidarity By Hyper Soul Of Space In Cancer's Recognition With (Extreme) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.30983.68009).
\bibitem{HG182}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Edge-Connectivity As Hyper Disclosure On Super Closure”, ResearchGate 2023, (doi: 10.13140/RG.2.2.28552.29445).
\bibitem{HG181}
Henry Garrett, “New Ideas On Super Uniform By Hyper Deformation Of Edge-Connectivity In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.10936.21761).
\bibitem{HG180}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Vertex-Connectivity As Hyper Leak On Super Structure”, ResearchGate 2023, (doi: 10.13140/RG.2.2.35105.89447).
\bibitem{HG179}
Henry Garrett, “New Ideas On Super System By Hyper Explosions Of Vertex-Connectivity In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.30072.72960).
\bibitem{HG178}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Tree-Decomposition As Hyper Forward On Super Returns”, ResearchGate 2023, (doi: 10.13140/RG.2.2.31147.52003).
\bibitem{HG177}
Henry Garrett, “New Ideas On Super Nodes By Hyper Moves Of Tree-Decomposition In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.32825.24163).
\bibitem{HG176}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By Chord As Hyper Excellence On Super Excess”, ResearchGate 2023, (doi: 10.13140/RG.2.2.13059.58401).
\bibitem{HG175}
Henry Garrett, “New Ideas On Super Gap By Hyper Navigations Of Chord In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.11172.14720).
\bibitem{HG174}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyper(i,j)-Domination As Hyper Controller On Super Waves”, ResearchGate 2023, (doi: 10.13140/RG.2.2.22011.80165).
\bibitem{HG173}
Henry Garrett, “New Ideas On Super Coincidence By Hyper Routes Of SuperHyper(i,j)-Domination In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.30819.84003).
\bibitem{HG172}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperEdge-Domination As Hyper Reversion On Super Indirection”, ResearchGate 2023, (doi: 10.13140/RG.2.2.10493.84962).
\bibitem{HG171}
Henry Garrett, “New Ideas On Super Obstacles By Hyper Model Of SuperHyperEdge-Domination In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.13849.29280).
\bibitem{HG170}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Domination As Hyper k-Actions On Super Patterns”, ResearchGate 2023, (doi: 10.13140/RG.2.2.19944.14086).
\bibitem{HG169}
Henry Garrett, “New Ideas On Super Harmony By Hyper k-Function Of SuperHyperK-Domination In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23299.58404).
\bibitem{HG168}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperK-Number As Hyper k-Partition On Super Layers”, ResearchGate 2023, (doi: 10.13140/RG.2.2.33103.76968).
\bibitem{HG167}
Henry Garrett, “New Ideas On Super Gradient By Hyper k-Class Of SuperHyperK-Number In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23037.44003).
\bibitem{HG166}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperOrder As Hyper Enumerations On Super Landmarks”, ResearchGate 2023, (doi: 10.13140/RG.2.2.35646.56641).
\bibitem{HG165}
Henry Garrett, “New Ideas On Super Analogous By Hyper Visions Of SuperHyperOrder In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.18030.48967).
\bibitem{HG164}
Henry Garrett, “New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperColoring As Hyper Categories On Super Neighbors”, ResearchGate 2023, (doi: 10.13140/RG.2.2.13973.81121).

\bibitem{HG163}
Henry Garrett, “New Ideas On Super Relations By Hyper Identifications Of SuperHyperColoring In Cancer's Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.34106.47047).

\bibitem{HG162} Henry Garrett, “New Ideas On Super Contradiction By Hyper Detection of SuperHyperDefensive In Cancer’s Neutrosophic Recognition and Neutrosophic SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.13397.09446).

\bibitem{HG161}
Henry Garrett, “New Ideas In Cancer’s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDimension As Hyper Distinguishing On Super Distances”, ResearchGate 2023, (doi: 10.13140/RG.2.2.31956.88961).

\bibitem{HG160} Henry Garrett, “New Ideas On Super Locations By Hyper Differing Of SuperHyperDimension In Cancer’s Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.15179.67361).

\bibitem{HG159}
Henry Garrett, “New Ideas In Cancer’s Recognition And Neutrosophic SuperHyperGraph By SuperHyperDominating As Hyper Closing On Super Messy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.21510.45125).
\bibitem{HG158}
Henry Garrett, “New Ideas On Super Missing By Hyper Searching Of SuperHyperDominating In Cancer’s Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.13121.84321).
\bibitem{HG157}
Henry Garrett, “New Ideas In Cancer’s Recognition And Neutrosophic SuperHyperGraph By SuperHyperConnected As Hyper Group On Super Surge”, ResearchGate 2023, (doi: 10.13140/RG.2.2.11758.69441).
\bibitem{HG156}
Henry Garrett, “New Ideas On Super Outbreak By Hyper Collections Of SuperHyperConnected In Cancer’s Recognition With (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.31891.35367).
\bibitem{HG155}
Henry Garrett, “New Ideas In Cancer’s Recognition And Neutrosophic SuperHyperGraph By SuperHyperTotal As Hyper Covering On Super Infections”, ResearchGate 2023, (doi: 10.13140/RG.2.2.19360.87048).
\bibitem{HG154}
Henry Garrett, “New Ideas On Super Extremism By Hyper Treatments Of SuperHyperTotal In Cancer’s Recognition with (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.32363.21286).
\bibitem{HG153}
  Henry Garrett, “New Ideas On Super Isolation By Hyper Perfectness Of SuperHyperPerfect In Cancer’s Recognition with (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.23266.81602).
\bibitem{HG152}
Henry Garrett, “New Ideas In Cancer’s Recognition And Neutrosophic SuperHyperGraph By SuperHyperPerfect As Hyper Idealism On Super Vacancy”, ResearchGate 2023, (doi: 10.13140/RG.2.2.19911.37285).
\bibitem{HG151}
Henry Garrett, “New Ideas In Cancer’s Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts”, ResearchGate 2023, (doi: 10.13140/RG.2.2.11050.90569).
\bibitem{HG150}
Henry Garrett, “New Ideas On Super connections By Hyper disconnections Of SuperHyperJoin In Cancer’s Recognition with (Neutrosophic) SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.17761.79206).
\bibitem{HG149}
Henry Garrett, “New Ideas On Super Mixed-Devastations By Hyper Decisions Of SuperHyperDuality In Cancer’s Neutrosophic Recognition and Neutrosophic SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.34953.52320).
\bibitem{HG148}
Henry Garrett, “New Ideas In Cancer’s Recognition As (Neutrosophic) SuperHyperGraph By SuperHyperDuality As Hyper Imaginations On Super Mixed-Illustrations”, ResearchGate 2023, (doi: 10.13140/RG.2.2.33275.80161).
\bibitem{HG147}
Henry Garrett, “New Ideas In Cancer’s Recognition As (Neutrosophic) SuperHyperGraph By Path SuperHyperColoring As Hyper Correction On Super Faults”, ResearchGate 2023, (doi: 10.13140/RG.2.2.30182.50241).
\bibitem{HG146}
Henry Garrett, “New Ideas On Super Reflections By Hyper Rotations Of Path SuperHyperColoring In Cancer’s Neutrosophic Recognition and Neutrosophic SuperHyperGraph”, ResearchGate 2023, (doi: 10.13140/RG.2.2.33459.30243).
\bibitem{HG145}
Henry Garrett, “New Ideas As Hyper Deformations On Super Chains In Cancer’s Neutrosophic Recognition and Neutrosophic SuperHyperGraph By SuperHyperDensity”, ResearchGate 2023, (doi: 10.13140/RG.2.2.13444.60806).
\bibitem{HG144}
Henry Garrett, “New Ideas As Hyper Ignorance By SuperHyperDensity On Super Resistances In Cancer’s Neutrosophic Recognition and Neutrosophic SuperHyperGraph”, ResearchGate 2023, (doi:10.13140/RG.2.2.16800.05123).
\bibitem{HG143}
Henry Garrett, “New Research On Cancer’s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-VI”, ResearchGate 2023, (doi: 10.13140/RG.2.2.29913.80482).
\bibitem{HG142}
Henry Garrett, “New Research On Cancer’s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-V”, ResearchGate 2023, (doi: 10.13140/RG.2.2.33269.24809).                
\bibitem{HG141}
Henry Garrett, “New Research On Cancer’s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-IV”, ResearchGate 2023, (doi: 10.13140/RG.2.2.34946.96960).
\bibitem{HG140}
Henry Garrett, “A Research On Cancer’s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-III”, ResearchGate 2023, (doi: 10.13140/RG.2.2.14814.31040).
\bibitem{HG139}
Henry Garrett, “A Research On Cancer’s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-II”, ResearchGate 2023, (doi: 10.13140/RG.2.2.15653.17125).
\bibitem{HG138}
Henry Garrett, “A Research On Cancer’s Recognition and Neutrosophic SuperHyperGraph By Eulerian SuperHyperCycles and Hamiltonian Sets As Hyper Covering Versus Super separations-I”, ResearchGate 2023, (doi: 10.13140/RG.2.2.25719.50089).
\bibitem{HG137}
Henry Garrett, “New Ideas On Super Disruptions In Cancer’s Extreme Recognition As Neutrosophic SuperHyperGraph By Hyper Plans Called SuperHyperConnectivities”, ResearchGate 2023, (doi: 10.13140/RG.2.2.29441.94562).
\bibitem{HG136}
Henry Garrett, “Cancer’s Neutrosophic Recognition As Neutrosophic SuperHyperGraph By SuperHyperConnectivities As Hyper Diagnosis On Super Mechanism”, ResearchGate 2023, (doi: 10.13140/RG.2.2.17252.24968).
\bibitem{HG135}
  Henry Garrett,“Cancer’s Recognition and (Neutrosophic) SuperHyperGraph By the Criteria of Eulerian and Hamiltonian Type-Sets As Hyper Modified Cycles On Super Mess”, ResearchGate 2023,(doi: 10.13140/RG.2.2.16652.59525).
\bibitem{HG134}
Henry Garrett,“Eulerian and Hamiltonian In Cancer’s Neutrosophic Recognition and Neutrosophic SuperHyperGraph On Super Interactions By Hyper Extensions of Cycles”, ResearchGate 2023,(doi: 10.13140/RG.2.2.34583.24485).

\bibitem{HG132} Henry Garrett,“SuperHyperGirth Type-Results on extreme SuperHyperGirth theory and (Neutrosophic) SuperHyperGraphs Toward Cancer’s extreme Recognition”, Preprints 2023, 2023010396 (doi: 10.20944/preprints202301.0396.v1).

\bibitem{HG131} Henry Garrett,“Neutrosophic SuperHyperGraphs Warns Hyper Landmark of neutrosophic SuperHyperGirth In Super Type-Versions of Cancer’s neutrosophic Recognition”, Preprints 2023, 2023010395 (doi: 10.20944/preprints202301.0395.v1).

\bibitem{HG130} Henry Garrett,“The Constructions of (Neutrosophic) SuperHyperGraphs on the Cancer’s Recognition in The Confrontation With Super Attacks In Hyper Situations By Implementing (Neutrosophic) 1-Failed SuperHyperForcing in The Technical Approaches to Neutralize SuperHyperViews”, ResearchGate 2023, (doi: 10.13140/RG.2.2.26240.51204).

\bibitem{HG129} Henry Garrett,“(Neutrosophic) 1-Failed SuperHyperForcing As the Entrepreneurs on Cancer’s Recognitions To Fail Forcing Style As the Super Classes With Hyper Effects In The Background of the Framework is So-Called (Neutrosophic) SuperHyperGraphs”, ResearchGate 2023, (doi: 10.13140/RG.2.2.12818.73925).

\bibitem{HG128} Henry Garrett,“Super Actions On The Types of Hyper Levels In The Sensible Neutrosophic SuperHyperGirth On Cancer’s Neutrosophic Recognition and Neutrosophic SuperHyperGraph”, ResearchGate 2023,(doi: 10.13140/RG.2.2.26836.88960).

\bibitem{HG127} Henry Garrett,“SuperHyperGirth Approaches on the Super Challenges on the Cancer’s Recognition In the Hyper Model of (Neutrosophic) SuperHyperGraph”, ResearchGate 2023,(doi: 10.13140/RG.2.2.36745.93289).

\bibitem{HG126}  Henry Garrett,“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{HG125} Henry Garrett,“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{HG124}  Henry Garrett,“Neutrosophic Version Of Separates Groups Of Cells In Cancer’s Recognition On Neutrosophic SuperHyperGraphs”, Preprints 2023, 2023010267 (doi: 10.20944/preprints202301.0267.v1).).

\bibitem{HG123}  Henry Garrett, “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{HG122} Henry Garrett,“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{HG121}  Henry Garrett, “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{HG120} Henry Garrett, “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{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{HG116}  Henry Garrett,“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{HG115}  Henry Garrett, “(Neutrosophic) 1-Failed SuperHyperForcing in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs”, Preprints 2023, 2023010105 (doi: 10.20944/preprints202301.0105.v1).

\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{HG112}  Henry Garrett, “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{HG111} Henry Garrett, “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{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{HG107} Henry Garrett, “Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer’s Neutrosophic Recognition And Beyond”, Preprints 2023, 2023010044

\bibitem{HG106} Henry Garrett, “(Neutrosophic) SuperHyperStable on Cancer’s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs”, Preprints 2023, 2023010043 (doi: 10.20944/preprints202301.0043.v1).


\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{HG982}  Henry Garrett, “(Neutrosophic) SuperHyperModeling of Cancer’s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances”, Preprints 2022, 2022120549 (doi: 10.20944/preprints202212.0549.v1).

\bibitem{HG98}  Henry Garrett, “(Neutrosophic) SuperHyperModeling of Cancer’s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances”, ResearchGate 2022, (doi: 10.13140/RG.2.2.19380.94084).


\bibitem{HG972}  Henry Garrett, “(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{HG97}  Henry Garrett, “(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer’s Recognitions And Related (Neutrosophic) SuperHyperClasses”, ResearchGate 2022, (doi: 10.13140/RG.2.2.14426.41923).


\bibitem{HG962} Henry Garrett, “SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer’s Recognitions”, Preprints 2022, 2022120500 (doi: 10.20944/preprints202212.0500.v1).


\bibitem{HG96} Henry Garrett, “SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer’s Recognitions”, ResearchGate 2022 (doi: 10.13140/RG.2.2.20993.12640).


\bibitem{HG952}  Henry Garrett,“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{HG95} Henry Garrett, “Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs And SuperHyperGraphs Alongside Applications in Cancer’s Treatments”, ResearchGate 2022 (doi: 10.13140/RG.2.2.23123.04641).

\bibitem{HG942}  Henry Garrett, “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{HG94} Henry Garrett, “SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses”, ResearchGate 2022 (doi: 10.13140/RG.2.2.23324.56966).

\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{HG155b}
Henry Garrett, “Hamiltonian-Cycle-Neighbor In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7804449).

\bibitem{HG154b}
Henry Garrett, “Hamiltonian-Cycle-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7793875).

\bibitem{HG153b}
 Henry Garrett, “Hamiltonian-Cycle-Cut In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7792307).

\bibitem{HG152b} Henry Garrett, “Hamiltonian-Neighbor In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7790728).

\bibitem{HG151b} Henry Garrett, “Hamiltonian-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7787712).

\bibitem{HG150b} Henry Garrett, “Hamiltonian-Cut In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7783791).

\bibitem{HG149b} Henry Garrett, “Trace-Neighbor In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7780123).

\bibitem{HG148b} Henry Garrett, “Trace-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7773119).

\bibitem{HG147b} Henry Garrett, “SuperHyperDuality”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7637762).

\bibitem{HG146b} Henry Garrett, “Trace-Cut In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7766174).

\bibitem{HG145b}Henry Garrett, “Edge-Neighbor In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7762232).

\bibitem{HG144b} Henry Garrett, “Edge-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7758601).

\bibitem{HG143b} Henry Garrett, “Edge-Cut In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7754661).

\bibitem{HG142b} Henry Garrett, “Vertex-Neighbor In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7750995) .

\bibitem{HG141b} Henry Garrett, “Vertex-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7749875).

\bibitem{HG140b} Henry Garrett, “Vertex-Cut In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7747236).

\bibitem{HG139b} Henry Garrett, “Stable-Neighbor In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7742587).

\bibitem{HG138b} Henry Garrett, “Stable-Decompositions In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7738635).

\bibitem{HG137b} Henry Garrett, “Stable-Cut In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7734719).

\bibitem{HG136b} Henry Garrett, “Clique-Neighbors In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7730484).

\bibitem{HG135b} Henry Garrett, “Clique-Decompositions In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7730469).

\bibitem{HG134b} Henry Garrett, “Clique-Cut In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7722865).

\bibitem{HG133b} Henry Garrett, “Space In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7713563).

\bibitem{HG132b} Henry Garrett, “Space In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7709116).

\bibitem{HG131b} Henry Garrett, “Edge-Connectivity In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7706415).

\bibitem{HG130b} Henry Garrett, “Vertex-Connectivity In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7706063).

\bibitem{HG129b} Henry Garrett, “Tree-Decomposition In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7701906).

\bibitem{HG128b} Henry Garrett, “Chord In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7700205).

\bibitem{HG127b} Henry Garrett, “(i,j)-Domination In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7694876).

\bibitem{HG126b} Henry Garrett, “Edge-Domination In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7679410).

\bibitem{HG125b} Henry Garrett, “K-Domination In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7675982).

\bibitem{HG124b} Henry Garrett, “K-Number In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7672388).

\bibitem{HG123b} Henry Garrett, “Order In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7668648).

\bibitem{HG122b} Henry Garrett, “Coloring In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7662810).

\bibitem{HG121b} Henry Garrett, “Dimension In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7659162).

\bibitem{HG120b} Henry Garrett, “Cancer In SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7653233).

\bibitem{HG119b} Henry Garrett, “SuperHyperWheel”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7653204).

\bibitem{HG118b} Henry Garrett, “SuperHyperMultipartite”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7653142).

\bibitem{HG117b} Henry Garrett, “SuperHyperBipartite”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7653117).

\bibitem{HG116b} Henry Garrett, “SuperHyperStar”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7653089).

\bibitem{HG115b} Henry Garrett, “SuperHyperCycle”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7651687).

\bibitem{HG114b} Henry Garrett, “SuperHyperPath”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7651619).

\bibitem{HG113b} Henry Garrett, “SuperHyperDomination”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7651439).

\bibitem{HG112b} Henry Garrett, “SuperHyperDominating”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7650729).

\bibitem{HG111b} Henry Garrett, “SuperHyperConnected”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7647868).

\bibitem{HG110b} Henry Garrett, “SuperHyperTotal”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7647017).

\bibitem{HG109b} Henry Garrett, “SuperHyperPerfect”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7644894).

\bibitem{HG108b} Henry Garrett, “SuperHyperJoin”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7641880).

\bibitem{HG107b} Henry Garrett, “Path SuperHyperColoring”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7632923).

\bibitem{HG106b} Henry Garrett, “SuperHyperDensity”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7623459).

\bibitem{HG105b} Henry Garrett, “Neutrosophic SuperHyperConnectivities”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7606416).

\bibitem{HG104b} Henry Garrett, “Extreme SuperHyperConnectivities”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7606416).

\bibitem{HG103b} Henry Garrett, “SuperHyperConnectivities”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7606404).

\bibitem{HG102b} Henry Garrett, “Neutrosophic SuperHyperCycle”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7580018).

\bibitem{HG101b} Henry Garrett, “Extreme SuperHyperCycle”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7580018).

\bibitem{HG100b} Henry Garrett, “Extreme SuperHyperCycle”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7580018).

\bibitem{HG99b} Henry Garrett, “SuperHyperCycle”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7579929).

\bibitem{HG98b} Henry Garrett, “Neutrosophic SuperHyperGirth”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7563170).

\bibitem{HG97b} Henry Garrett, “Extreme SuperHyperGirth”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7563164).
   
   \bibitem{HG96b} Henry Garrett, “SuperHyperGirth”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7563160).
   
   \bibitem{HG95b} Henry Garrett, “Extreme SuperHyperGirth”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7563160).
   
   \bibitem{HG94b} Henry Garrett, “Overlook On SuperHyperGirth”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7563160).
   
   \bibitem{HG93b} Henry Garrett, “Neutrosophic SuperHyperMatching”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7557063).
   
   \bibitem{HG92b} Henry Garrett, “Extreme SuperHyperMatching”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7557009).
   
   \bibitem{HG91b} Henry Garrett, “Overlook On SuperHyperMatching”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7539484).
   
   \bibitem{HG90b} Henry Garrett, “Neutrosophic Failed SuperHyperClique”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7523390).
   
   \bibitem{HG89b} Henry Garrett, “Extreme Failed SuperHyperClique”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7523390).
   
   \bibitem{HG88b} Henry Garrett, “Overlook On Failed SuperHyperClique”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7523390).
   
   \bibitem{HG87b} Henry Garrett, “Extreme SuperHyperClique”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7574952).
   
  \bibitem{HG86b} Henry Garrett, “Neutrosophic SuperHyperClique”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7574992).
 
   \bibitem{HG85b} Henry Garrett, “Extreme SuperHyperClique”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7523357).
   
   \bibitem{HG84b} Henry Garrett, “Overlook On SuperHyperClique”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7523357).
   
   \bibitem{HG83b} Henry Garrett, “Neutrosophic Failed SuperHyperStable”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7504782).
   
   \bibitem{HG82b} Henry Garrett, “Extreme Failed SuperHyperStable”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7504782).
   
   \bibitem{HG81b} Henry Garrett, “Overlook On Failed SuperHyperStable”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7504782).
   
   \bibitem{HG80b} Henry Garrett, “Neutrosophic SuperHyperStable”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7499395).
   
   \bibitem{HG79b} Henry Garrett, “Extreme SuperHyperStable”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7499395).
   
   \bibitem{HG78b} Henry Garrett, “Overlook On SuperHyperStable”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7499395).
   
 \bibitem{HG77b} Henry Garrett, “Neutrosophic Failed SuperHyperForcing”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7497450).
 
  \bibitem{HG76b} Henry Garrett, “Extreme Failed SuperHyperForcing”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7497450).
 
   \bibitem{HG75b} Henry Garrett, “Neutrosophic SuperHyperForcing”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7494862).
   
  \bibitem{HG74b} Henry Garrett, “Extreme SuperHyperForcing”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7494862).
 
   \bibitem{HG73b} Henry Garrett, “Overlook On SuperHyperForcing”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7494862).
   
   \bibitem{HG72b} Henry Garrett, “Neutrosophic SuperHyperAlliances”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7493845).
   
   \bibitem{HG71b} Henry Garrett, “Extreme SuperHyperAlliances”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7493845).
   
 \bibitem{HG70b} Henry Garrett, “Overlook On SuperHyperAlliances”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7493845).
 
   \bibitem{HG69b} Henry Garrett, “SuperHyperMatching”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7539484).
   
   \bibitem{HG68b} Henry Garrett, “Failed SuperHyperClique”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7523390).
   
   \bibitem{HG67b} Henry Garrett, “SuperHyperClique”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7523357).  
   
   \bibitem{HG66b} Henry Garrett, “Failed SuperHyperStable”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7504782).
   
 \bibitem{HG65b} Henry Garrett, “SuperHyperStable”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7499395).
 
   \bibitem{HG64b} Henry Garrett, “Failed SuperHyperForcing”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7497450).
   
   \bibitem{HG63b} Henry Garrett, “SuperHyperForcing”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7494862).
   
 \bibitem{HG62b} Henry Garrett, “SuperHyperAlliances”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7493845).
 
\bibitem{HG61b} Henry Garrett, “SuperHyperGraphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7480110).

   \bibitem{HG60b} Henry Garrett, “Neut. SuperHyperEdges”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.7378758).
   
 \bibitem{HG32b} Henry Garrett, “Beyond Neutrosophic Graphs”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.6320305).
   
 \bibitem{HG44b} Henry Garrett, “Neutrosophic Duality”. Dr. Henry Garrett, 2023 (doi: 10.5281/zenodo.6677173).

\end{thebibliography}
\end{document}

Files

Files (2.7 MB)

Name Size Download all
md5:1005dcec9d5919dc3e3dc6a2569ea982
2.7 MB Download