New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts

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\fancyhead[LE,RO]{Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA }
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New Ideas In Cancer's Recognition And Neutrosophic SuperHyperGraph By SuperHyperJoin As Hyper Separations On Super Sorts
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Henry Garrett · Independent Researcher · Department of Mathematics · DrHenryGarrett@gmail.com · Manhattan, NY, USA
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\section*{ABSTRACT}
In this scientific research, (Different Neutrosophic Types of Neutrosophic SuperHyperJoin). Assume a Neutrosophic SuperHyperGraph (NSHG) $S$ is an ordered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperSet $V^{\prime }=\{V_1,V_2,\dots ,V_s\}$ and $E^{\prime }=\{E_1,E_2,\dots ,E_z\}.$ Then either $V^{\prime }$ or $E^{\prime }$ is called Neutrosophic e-SuperHyperJoin if $\mathrm{\forall }{E}_i\in E_{ESHG:(V,E)}\setminus E^{\prime },\mathrm{\exists }{E}_j\in E^{\prime },$ such that $V_a\in E_i,E_j;$ and $\mathrm{\forall }{E}_i,E_j\in E^{\prime },$ such that $V_a\notin E_i,E_j;$ Neutrosophic re-SuperHyperJoin if $\mathrm{\forall }{E}_i\in E_{ESHG:(V,E)}\setminus E^{\prime },\mathrm{\exists }{E}_j\in E^{\prime },$ such that $V_a\in E_i,E_j;$ $\mathrm{\forall }{E}_i,E_j\in E^{\prime },$ such that $V_a\notin E_i,E_j;$ and $|E_i{|}_{\text{NEUTROSOPIC CARDINALITY}}=|E_j{|}_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic v-SuperHyperJoin if $\mathrm{\forall }{V}_i\in E_{ESHG:(V,E)}\setminus V^{\prime },\mathrm{\exists }{V}_j\in V^{\prime },$ such that $V_i,V_j\notin E_a;$ and $\mathrm{\forall }{V}_i,V_j\in V^{\prime },$ such that $V_i,V_j\notin E_a;$ Neutrosophic rv-SuperHyperJoin if $\mathrm{\forall }{V}_i\in E_{ESHG:(V,E)}\setminus V^{\prime },\mathrm{\exists }{V}_j\in V^{\prime },$ such that $V_i,V_j\in E_a;$ $\mathrm{\forall }{V}_i,V_j\in V^{\prime },$ such that $V_i,V_j\notin E_a;$ and $|V_i{|}_{\text{NEUTROSOPIC CARDINALITY}}=|V_j{|}_{\text{NEUTROSOPIC CARDINALITY}};$ Neutrosophic SuperHyperJoin if it's either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin. ((Neutrosophic) SuperHyperJoin).
 Assume a Neutrosophic SuperHyperGraph (NSHG) $S$
is an ordered pair $S=(V,E).$ Consider a Neutrosophic SuperHyperEdge (NSHE) $E=\{V_1,V_2,\dots ,V_s\}.$
Then $E$ is called an Extreme SuperHyperJoin if it's either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperEdges in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; a Neutrosophic SuperHyperJoin if it's either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a  Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality  consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; an Extreme SuperHyperJoin SuperHyperPolynomial  if it's either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperEdges of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperJoin SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperEdges of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient; an Extreme R-SuperHyperJoin if it's either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the maximum Extreme cardinality of an Extreme SuperHyperSet $S$ of high Extreme cardinality of the Extreme SuperHyperVertices in the consecutive Extreme sequence of Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; a Neutrosophic R-SuperHyperJoin if it's either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; an Extreme R-SuperHyperJoin SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for an Extreme SuperHyperGraph $NSHG:(V,E)$ is the Extreme SuperHyperPolynomial contains the Extreme coefficients defined as the Extreme number of the maximum Extreme cardinality of the Extreme SuperHyperVertices of an Extreme SuperHyperSet $S$ of high Extreme cardinality consecutive Extreme SuperHyperEdges and Extreme SuperHyperVertices such that they form the Extreme SuperHyperJoin; and the Extreme power is corresponded to its Extreme coefficient; a Neutrosophic SuperHyperJoin SuperHyperPolynomial if it's either of Neutrosophic e-SuperHyperJoin, Neutrosophic re-SuperHyperJoin, Neutrosophic v-SuperHyperJoin, and Neutrosophic rv-SuperHyperJoin and $\mathcal{C}(NSHG)$ for a Neutrosophic SuperHyperGraph $NSHG:(V,E)$ is  the Neutrosophic SuperHyperPolynomial contains the Neutrosophic coefficients defined as the Neutrosophic number of the maximum Neutrosophic cardinality of the Neutrosophic SuperHyperVertices of a Neutrosophic SuperHyperSet $S$ of high Neutrosophic cardinality consecutive Neutrosophic SuperHyperEdges and Neutrosophic SuperHyperVertices such that they form the Neutrosophic SuperHyperJoin; and the Neutrosophic power is corresponded to its Neutrosophic coefficient. In this scientific research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperJoin  and Neutrosophic SuperHyperJoin. 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 $\delta -$SuperHyperJoin is a maximal    of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (Neutrosophic) cardinalities of  SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)|>|S\cap (V\setminus N(s))|+\delta ;$ and $|S\cap N(s)|<|S\cap (V\setminus N(s))|+\delta .$
The first Expression, holds if $S$ is an $\delta -$SuperHyperOffensive. And the second Expression, holds if $S$ is an $\delta -$SuperHyperDefensive; a Neutrosophic $\delta -$SuperHyperJoin 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 $s\in S$ there are: $|S\cap N(s){|}_{Neutrosophic}>|S\cap (V\setminus N(s)){|}_{Neutrosophic}+\delta ;$ and
$|S\cap N(s){|}_{Neutrosophic}<|S\cap (V\setminus N(s)){|}_{Neutrosophic}+\delta .$
The first Expression, holds if $S$ is a Neutrosophic $\delta -$SuperHyperOffensive. And the second Expression, holds if $S$ is a Neutrosophic $\delta -$SuperHyperDefensive
  It's useful to define a ``Neutrosophic'' version of a SuperHyperJoin . Since there's more ways to get type-results to make a SuperHyperJoin  more understandable. For the sake of having Neutrosophic SuperHyperJoin, there's a need to ``redefine'' the notion of a ``SuperHyperJoin ''. 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 SuperHyperJoin . It's redefined a Neutrosophic SuperHyperJoin  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 SuperHyperJoin . 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 SuperHyperJoin until the SuperHyperJoin, then it's officially called a ``SuperHyperJoin'' but otherwise, it isn't a SuperHyperJoin . There are some instances about the clarifications for the main definition titled a ``SuperHyperJoin ''. These two examples get more scrutiny and discernment since there are characterized in the disciplinary ways of the SuperHyperClass based on a SuperHyperJoin . For the sake of having a Neutrosophic SuperHyperJoin, there's a need to ``redefine'' the notion of a ``Neutrosophic SuperHyperJoin'' and a ``Neutrosophic SuperHyperJoin ''. 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 SuperHyperJoin  are redefined to a ``Neutrosophic SuperHyperJoin'' 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 SuperHyperJoin  more understandable. Assume a Neutrosophic SuperHyperGraph. There are some Neutrosophic SuperHyperClasses if the intended Table holds. Thus  SuperHyperPath,  SuperHyperJoin, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and   SuperHyperWheel, are
``Neutrosophic SuperHyperPath'', ``Neutrosophic SuperHyperJoin'', ``Neutrosophic SuperHyperStar'', ``Neutrosophic SuperHyperBipartite'', ``Neutrosophic SuperHyperMultiPartite'', and ``Neutrosophic SuperHyperWheel'' if the intended Table holds.  A SuperHyperGraph has a ``Neutrosophic SuperHyperJoin'' where it's the strongest [the maximum Neutrosophic value from all the SuperHyperJoin  amid the maximum value amid all SuperHyperVertices from a SuperHyperJoin .] SuperHyperJoin . 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 SuperHyperJoin 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(-/SuperHyperJoin, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,  SuperHyperWheel). The aim is to find either the longest SuperHyperJoin  or the strongest SuperHyperJoin  in those Neutrosophic SuperHyperModels. For the longest SuperHyperJoin, called SuperHyperJoin, and the strongest SuperHyperJoin, called Neutrosophic SuperHyperJoin, 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 SuperHyperJoin. There isn't any formation of any SuperHyperJoin but literarily, it's the deformation of any SuperHyperJoin. It, literarily, deforms and it doesn't form.  A basic familiarity with Neutrosophic  SuperHyperJoin theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.
\ \vspace{4mm}
\textbf{Keywords:} Neutrosophic SuperHyperGraph, SuperHyperJoin, Cancer's Neutrosophic Recognition
   \
\textbf{AMS Subject Classification:} 05C17, 05C22, 05E45
\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 date back on January 22, 2023.
\
First article is titled ``properties of SuperHyperGraph and neutrosophic SuperHyperGraph''  in \textbf{Ref.} \cite{HG1} by Henry Garrett (2022). It's first step toward the research on neutrosophic SuperHyperGraphs. This research article is published on the journal ``Neutrosophic Sets and Systems'' in issue 49 and the pages 531-561. In this research article, different types of notions like dominating, resolving, coloring, Eulerian(Hamiltonian) neutrosophic path, n-Eulerian(Hamiltonian) neutrosophic path, zero forcing number, zero forcing neutrosophic- number, independent number, independent neutrosophic-number, clique number, clique neutrosophic-number, matching number, matching neutrosophic-number, girth, neutrosophic girth, 1-zero-forcing number, 1-zero- forcing neutrosophic-number, failed 1-zero-forcing number, failed 1-zero-forcing neutrosophic-number, global- offensive alliance, t-offensive alliance, t-defensive alliance, t-powerful alliance, and global-powerful alliance are defined in SuperHyperGraph and neutrosophic SuperHyperGraph. Some Classes of SuperHyperGraph and Neutrosophic SuperHyperGraph are cases of research. Some results are applied in family of SuperHyperGraph and neutrosophic SuperHyperGraph. Thus this research article has concentrated on the vast notions and introducing the majority of notions.
\
The seminal paper and groundbreaking article is titled ``neutrosophic co-degree and neutrosophic degree alongside chromatic numbers in the setting of some classes related to neutrosophic hypergraphs'' in \textbf{Ref.} \cite{HG2} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on general forms without using neutrosophic classes of neutrosophic SuperHyperGraph. It's published in prestigious and fancy journal is entitled “Journal of Current Trends in Computer Science Research (JCTCSR)” with abbreviation ``J Curr Trends Comp Sci Res'' in volume 1 and issue 1 with pages 06-14. The research article studies deeply with choosing neutrosophic hypergraphs instead of neutrosophic SuperHyperGraph. It's the breakthrough toward independent results based on initial background.
\
The seminal paper and groundbreaking article is titled ``Super Hyper Dominating and Super Hyper Resolving on Neutrosophic Super Hyper Graphs and Their Directions in Game Theory and Neutrosophic Super Hyper Classes'' in \textbf{Ref.} \cite{HG3} by Henry Garrett (2022). In this research article, a novel approach is implemented on SuperHyperGraph and neutrosophic SuperHyperGraph based on fundamental SuperHyperNumber and using neutrosophic SuperHyperClasses of neutrosophic SuperHyperGraph. It's published in prestigious and fancy journal is entitled “Journal of Mathematical Techniques and Computational Mathematics(JMTCM)” with abbreviation ``J Math Techniques Comput Math'' in volume 1 and issue 3 with pages 242-263. The research article studies deeply with choosing directly neutrosophic SuperHyperGraph and SuperHyperGraph. It's the breakthrough toward independent results based on initial background and fundamental SuperHyperNumbers.
\
In some articles are titled ``0039 | Closing Numbers and Super-Closing Numbers as (Dual)Resolving and (Dual)Coloring alongside (Dual)Dominating in (Neutrosophic)n-SuperHyperGraph'' in \textbf{Ref.} \cite{HG4} by Henry Garrett (2022),  ``0049 | (Failed)1-Zero-Forcing Number in Neutrosophic Graphs'' in \textbf{Ref.} \cite{HG5} by Henry Garrett (2022),  ``Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer’s Recognition as the Model in The Setting of (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG6} by Henry Garrett (2022), ``Uncertainty On The Act And Effect Of Cancer Alongside The Foggy Positions Of Cells Toward Neutrosophic Failed SuperHyperClique inside Neutrosophic SuperHyperGraphs Titled Cancer’s Recognition'' in \textbf{Ref.} \cite{HG7} by Henry Garrett (2022), ``Neutrosophic Version Of Separates Groups Of Cells In Cancer’s Recognition On Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG8} by Henry Garrett (2022), ``The Shift Paradigm To Classify Separately The Cells and Affected Cells Toward The Totality Under Cancer’s Recognition By New Multiple Definitions On the Sets Polynomials Alongside Numbers In The (Neutrosophic) SuperHyperMatching Theory Based on SuperHyperGraph and Neutrosophic SuperHyperGraph'' in \textbf{Ref.} \cite{HG9} by Henry Garrett (2022), ``Breaking the Continuity and Uniformity of Cancer In The Worst Case of Full Connections With Extreme Failed SuperHyperClique In Cancer’s Recognition Applied in (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG10} by Henry Garrett (2022), ``Neutrosophic Failed SuperHyperStable as the Survivors on the Cancer’s Neutrosophic Recognition Based on Uncertainty to All Modes in Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG11} by Henry Garrett (2022), ``Extremism of the Attacked Body Under the Cancer's Circumstances Where Cancer's Recognition Titled (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG13} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints'' in \textbf{Ref.} \cite{HG14} by Henry Garrett (2022),  ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer’s Neutrosophic Recognition And Beyond'' in \textbf{Ref.} \cite{HG15} by Henry Garrett (2022),  ``(Neutrosophic) SuperHyperStable on Cancer’s Recognition by Well- SuperHyperModelled (Neutrosophic) SuperHyperGraphs
'' in \textbf{Ref.} \cite{HG16} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints'' in \textbf{Ref.} \cite{HG12} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG17} by Henry Garrett (2022), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints'' in \textbf{Ref.} \cite{HG18} by Henry Garrett (2022),``(Neutrosophic) SuperHyperModeling of Cancer’s Recognitions Featuring (Neutrosophic) SuperHyperDefensive SuperHyperAlliances'' in \textbf{Ref.} \cite{HG19} by Henry Garrett (2022), ``(Neutrosophic) SuperHyperAlliances With SuperHyperDefensive and SuperHyperOffensive Type-SuperHyperSet On (Neutrosophic) SuperHyperGraph With (Neutrosophic) SuperHyperModeling of Cancer’s Recognitions And Related (Neutrosophic) SuperHyperClasses'' in \textbf{Ref.} \cite{HG20} by Henry Garrett (2022), ``SuperHyperGirth on SuperHyperGraph and Neutrosophic SuperHyperGraph With SuperHyperModeling of Cancer’s Recognitions'' in \textbf{Ref.} \cite{HG21} by Henry Garrett (2022), ``Some SuperHyperDegrees and Co-SuperHyperDegrees on Neutrosophic SuperHyperGraphs and SuperHyperGraphs Alongside Applications in Cancer’s Treatments'' in \textbf{Ref.} \cite{HG22} by Henry Garrett (2022), ``SuperHyperDominating and SuperHyperResolving on Neutrosophic SuperHyperGraphs And Their Directions in Game Theory and Neutrosophic SuperHyperClasses'' in \textbf{Ref.} \cite{HG23} by Henry Garrett (2022), ``SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer’s Recognition In Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG24} by Henry Garrett (2023), ``The Focus on The Partitions Obtained By Parallel Moves In The Cancer's Extreme Recognition With Different Types of Extreme SuperHyperMatching Set and Polynomial on (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG25} by Henry Garrett (2023), ``Extreme Failed SuperHyperClique Decides the Failures on the Cancer's Recognition in the Perfect Connections of Cancer's Attacks By SuperHyperModels Named (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG26} by Henry Garrett (2023), ``Indeterminacy On The All Possible Connections of Cells In Front of Cancer's Attacks In The Terms of Neutrosophic Failed SuperHyperClique on Cancer's Recognition called Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG27} by Henry Garrett (2023), ``Perfect Directions Toward Idealism in Cancer's Neutrosophic Recognition Forwarding Neutrosophic SuperHyperClique on Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG28} by Henry Garrett (2023), ``Demonstrating Complete Connections in Every Embedded Regions and Sub-Regions in the Terms of Cancer's Recognition and (Neutrosophic) SuperHyperGraphs With (Neutrosophic) SuperHyperClique'' in \textbf{Ref.} \cite{HG29} by Henry Garrett (2023), ``Different Neutrosophic Types of Neutrosophic Regions titled neutrosophic Failed SuperHyperStable in Cancer’s Neutrosophic Recognition modeled in the Form of Neutrosophic SuperHyperGraphs'' in \textbf{Ref.} \cite{HG30} by Henry Garrett (2023), ``Using the Tool As (Neutrosophic) Failed SuperHyperStable To SuperHyperModel Cancer's Recognition Titled (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG31} by Henry Garrett (2023), ``Neutrosophic Messy-Style SuperHyperGraphs To Form Neutrosophic SuperHyperStable To Act on Cancer’s Neutrosophic Recognitions In Special ViewPoints'' in \textbf{Ref.} \cite{HG32} by Henry Garrett (2023), ``(Neutrosophic) SuperHyperStable on Cancer’s Recognition by Well-SuperHyperModelled (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG33} by Henry Garrett (2023), ``Neutrosophic 1-Failed SuperHyperForcing in the SuperHyperFunction To Use Neutrosophic SuperHyperGraphs on Cancer’s Neutrosophic Recognition And Beyond'' in \textbf{Ref.} \cite{HG34} by Henry Garrett (2022),  ``(Neutrosophic) 1-Failed SuperHyperForcing in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG35} by Henry Garrett (2022), ``Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs'' in \textbf{Ref.} \cite{HG36} by Henry Garrett (2022), ``Basic Neutrosophic Notions Concerning SuperHyperDominating and Neutrosophic SuperHyperResolving in SuperHyperGraph'' in \textbf{Ref.} \cite{HG37} by Henry Garrett (2022), ``Initial Material of Neutrosophic Preliminaries to Study Some Neutrosophic Notions Based on Neutrosophic SuperHyperEdge (NSHE) in Neutrosophic SuperHyperGraph (NSHG)''  in \textbf{Ref.} \cite{HG38} by Henry Garrett (2022),  there are some endeavors to formalize the basic SuperHyperNotions about neutrosophic SuperHyperGraph and SuperHyperGraph.    
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Some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG39} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 3230 readers in Scribd. It's titled ``Beyond Neutrosophic Graphs'' and published by Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United State. This research book covers different types of notions and settings in neutrosophic graph theory and neutrosophic SuperHyperGraph theory.
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Also, some scientific studies and scientific researches about neutrosophic graphs, are proposed as book in \textbf{Ref.} \cite{HG40} by Henry Garrett (2022) which is indexed by Google Scholar and has more than 4117 readers in Scribd. It's titled ``Neutrosophic Duality'' and published by Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. This research book presents different types of notions SuperHyperResolving and SuperHyperDominating in the setting of duality in neutrosophic graph theory and neutrosophic SuperHyperGraph theory. This research book has scrutiny on the complement of the intended set and the intended set, simultaneously. It's smart to consider a set but acting on its complement that what's done in this research book which is popular in the terms of high readers in Scribd.
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See the seminal scientific researches \cite{HG1,HG2,HG3}. The formalization of the notions on the framework of Extreme SuperHyperJoin theory, Neutrosophic SuperHyperJoin theory, and (Neutrosophic) SuperHyperGraphs theory at \cite{HG4,HG5,HG6,HG7,HG8,HG9,HG10,HG11,HG12,HG13,HG14,HG15,HG16,HG17,HG18,HG19,HG20,HG21,HG22,HG23,HG24,HG25,HG26,HG27,HG28,HG29,HG30,HG31,HG32,HG33,HG34,HG35,HG36,HG37,HG38}. Two popular scientific research books in Scribd in the terms of high readers, 3230 and 4117 respectively,  on neutrosophic science is on \cite{HG39,HG40}.
\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 ``Neutrosophic 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 ``Neutrosophic 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 Neutrosophic 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 ``  SuperHyperJoin'' 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 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 general models. 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 (-/SuperHyperJoin, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,  SuperHyperWheel). The aim is to find either the optimal   SuperHyperJoin or the Neutrosophic   SuperHyperJoin in those Neutrosophic SuperHyperModels. Some general results are introduced. Beyond that in SuperHyperStar, all possible Neutrosophic 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 SuperHyperJoin. There isn't any formation of any SuperHyperJoin but literarily, it's the deformation of any SuperHyperJoin. It, literarily, deforms and it doesn't form.
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It's motivation to find notions to use in this dense model is titled ``SuperHyperGraphs''. Thus it motivates us to define different types of ``  SuperHyperJoin'' and ``Neutrosophic   SuperHyperJoin'' on ``SuperHyperGraph'' and ``Neutrosophic 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.
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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 Neutrosophic 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,   SuperHyperJoin and Neutrosophic   SuperHyperJoin, are figured out in sections ``  SuperHyperJoin'' and ``Neutrosophic   SuperHyperJoin''. In the sense of tackling on getting results and in order to make sense about continuing the research, the ideas of SuperHyperUniform and Neutrosophic 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 Neutrosophic 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 Neutrosophic SuperHyperGraph, in the sections ``Results on SuperHyperClasses'' and ``Results on Neutrosophic 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'',
``  SuperHyperJoin'', ``Neutrosophic   SuperHyperJoin'', ``Results on SuperHyperClasses'' and ``Results on Neutrosophic 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, ``  SuperHyperJoin''. 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{Neutrosophic 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}.
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In this subsection, the basic material which is used in this scientific research, is presented. Also, the new ideas and their clarifications are elicited.
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If we choose different types of binary operations, then we could get hugely diverse types of general forms of Neutrosophic SuperHyperGraph (NSHG).
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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.
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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}

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For the sake of having a Neutrosophic SuperHyperJoin, 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.
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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.
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It's useful to define a ``Neutrosophic'' version of a Neutrosophic SuperHyperJoin. Since there's more ways to get type-results to make a Neutrosophic SuperHyperJoin more Neutrosophicly understandable.
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For the sake of having a Neutrosophic SuperHyperJoin, there's a need to ``\textbf{redefine}'' the Neutrosophic notion of ``Neutrosophic SuperHyperJoin''. 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.
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\section{
Neutrosophic SuperHyperJoin But As The Extensions Excerpt From Dense And Super Forms}
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\section{The Neutrosophic Departures on The Theoretical Results Toward Theoretical Motivations}
The previous Neutrosophic approach apply on the upcoming Neutrosophic results on Neutrosophic SuperHyperClasses.
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\begin{proposition}
Assume a connected Neutrosophic SuperHyperBipartite $ESHB:(V,E).$ Then
$$\begin{array}{rcl}& & \mathcal{C}(NSHG{)}_{\text{Neutrosophic Quasi-SuperHyperJoin}}\\ & & =\text{(PERFECT MATCHING)}.\\ & & \{E_i\in E_{{P_i}^{ESHG:(V,E)}},\\ & & \mathrm{\forall }{P_i}^{ESHG:(V,E)},|{P_i}^{ESHG:(V,E)}|=\underset{i}{min}|{P_i}^{ESHG:(V,E)}\in P^{ESHG:(V,E)}|\}.\\ & & \mathcal{C}(NSHG{)}_{\text{Neutrosophic Quasi-SuperHyperJoin}}\\ & & =\text{(OTHERWISE)}.\\ & & \{\},\\ & & \text{If}\mathrm{\exists }{P_i}^{ESHG:(V,E)},|{P_i}^{ESHG:(V,E)}|\ne \underset{i}{min}|{P_i}^{ESHG:(V,E)}\in P^{ESHG:(V,E)}|.\\ & & \mathcal{C}(NSHG{)}_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}\\ & & =\text{(PERFECT MATCHING)}.\\ & & =(\sum _{i=|P^{ESHG:(V,E)}|}(\underset{i}{min}|{P_i}^{ESHG:(V,E)}\in P^{ESHG:(V,E)}|)\text{choose}|{P_i}^{ESHG:(V,E)}|)\\ & & z^{min|{P_i}^{ESHG:(V,E)}\in P^{ESHG:(V,E)}|}\\ & & \text{where}\mathrm{\forall }{P_i}^{ESHG:(V,E)},|{P_i}^{ESHG:(V,E)}|\\ & & =\underset{i}{min}|{P_i}^{ESHG:(V,E)}\in P^{ESHG:(V,E)}|\}.\\ & & \mathcal{C}(NSHG{)}_{\text{Neutrosophic SuperHyperJoin SuperHyperPolynomial}}\\ & & =\text{(OTHERWISE)}0.\\ & & \mathcal{C}(NSHG{)}_{\text{Neutrosophic Quasi-SuperHyperJoin}}\\ & & =\{V_i^{EXTERNAL}\in V_{{P_i}^{ESHG:(V,E)}}^{EXTERNAL},V_i^{EXTERNAL}\in V_{{P_i}^{ESHG:(V,E)}}^{EXTERNAL},i\ne j\}.\\ & & \mathcal{C}(NSHG{)}_{\text{Neutrosophic Quasi-SuperHyperJoin SuperHyperPolynomial}}\\ & & =\sum _{|V_{ESHG:(V,E)}^{EXTERNAL}{|}_{\text{Neutrosophic Cardinality}}}=(\sum _{i=|P^{ESHG:(V,E)}|}(|{P_i}^{ESHG:(V,E)}|\text{choose}2)=z^2.\end{array}$$

\end{proposition}
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\section{The Surveys of Mathematical Sets On The Results But As The Initial Motivation}
For the SuperHyperJoin,  Neutrosophic SuperHyperJoin, and the Neutrosophic SuperHyperJoin, some general results are introduced.
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\begin{corollary}
 Assume Neutrosophic SuperHyperJoin. Then
 $$\begin{array}{rcl}& & NeutrosophicSuperHyperJoin=\\ & & \{theSuperHyperJoinoftheSuperHyperVertices|\\ & & max|SuperHyperOffensive\\ & & SuperHyperJoin\\ & & {|}_{NeutrosophiccardinalityamidthoseSuperHyperJoin.}\}\end{array}$$
plus one Neutrosophic SuperHypeNeighbor to one. Where ${\sigma }_i$ 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}
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 \section{Neutrosophic Applications in Cancer's Neutrosophic Recognition}
The cancer is the Neutrosophic disease but the Neutrosophic model is going to figure out what's going on this Neutrosophic phenomenon. The special Neutrosophic case of this Neutrosophic 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 Neutrosophic recognition of the cancer could help to find some Neutrosophic treatments for this Neutrosophic disease.
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In the following, some Neutrosophic steps are Neutrosophic devised on this disease.
\begin{description}
 \item[Step 1. (Neutrosophic Definition)] The Neutrosophic recognition of the cancer in the long-term Neutrosophic function.
  \item[Step 2. (Neutrosophic Issue)] The specific region has been assigned by the Neutrosophic model [it's called Neutrosophic SuperHyperGraph] and the long Neutrosophic 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.
 \item[Step 3. (Neutrosophic Model)]  
There are some specific Neutrosophic models, which are well-known and they've got the names, and some general Neutrosophic models. The moves and the Neutrosophic traces of the cancer on the complex tracks and between complicated groups of cells could be fantasized by a Neutrosophic SuperHyperPath(-/SuperHyperJoin, SuperHyperStar, SuperHyperBipartite, SuperHyperMultipartite,  SuperHyperWheel). The aim is to find either the Neutrosophic   SuperHyperJoin or the Neutrosophic   SuperHyperJoin in those Neutrosophic Neutrosophic SuperHyperModels.
  \section{Case 1: The Initial Neutrosophic Steps Toward Neutrosophic SuperHyperBipartite as  Neutrosophic SuperHyperModel}

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

     \item[Step 4. (Neutrosophic Solution)]
In the Neutrosophic Figure $\text{(???)}$, the Neutrosophic SuperHyperMultipartite is Neutrosophic highlighted and  Neutrosophic featured.
$$\text{Unknown environment 'figure'}$$
\
 By using the Neutrosophic Figure $\text{(???)}$ and the Table $\text{(???)}$, the Neutrosophic SuperHyperMultipartite is obtained.
 \
 The obtained Neutrosophic SuperHyperSet, by the Neutrosophic Algorithm in previous result, of the Neutrosophic SuperHyperVertices of the connected Neutrosophic SuperHyperMultipartite $ESHM:(V,E),$ in the Neutrosophic SuperHyperModel $\text{(???)}$, is the  Neutrosophic SuperHyperJoin.
$$\text{Unknown environment 'table'}$$
     \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   SuperHyperJoin and the Neutrosophic   SuperHyperJoin are defined on a real-world application, titled ``Cancer's Recognitions''.
$$\text{Unknown environment 'question'}$$
$$\text{Unknown environment 'question'}$$
$$\text{Unknown environment 'question'}$$
$$\text{Unknown environment 'question'}$$
$$\text{Unknown environment 'problem'}$$
$$\text{Unknown environment 'problem'}$$
$$\text{Unknown environment 'problem'}$$
\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 Neutrosophic SuperHyperGraphs more understandable. In this endeavor, two SuperHyperNotions are defined on the   SuperHyperJoin. For that sake in the second definition, the main definition of the Neutrosophic SuperHyperGraph is redefined on the position of the alphabets. Based on the new definition for the Neutrosophic SuperHyperGraph, the new SuperHyperNotion, Neutrosophic   SuperHyperJoin, finds the convenient background to implement some results based on that. Some SuperHyperClasses and some Neutrosophic 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,   SuperHyperJoin, the new SuperHyperClasses and SuperHyperClasses, are introduced. Some general results are gathered in the section on the   SuperHyperJoin and the Neutrosophic   SuperHyperJoin. 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 Neutrosophic 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 ``  SuperHyperJoin'' 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.
$$\text{Unknown environment 'table'}$$
In the Table $\text{(???)}$, benefits and avenues for this research are, figured out, pointed out and spoken out.
      
\begin{thebibliography}{595}

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

\bibitem{HG39} Henry Garrett, (2022). ``\textit{Beyond Neutrosophic Graphs}'', Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grandview Heights, Ohio 43212 United States. ISBN: 979-1-59973-725-6 (http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf).
      
 \bibitem{HG40} Henry Garrett, (2022). ``\textit{Neutrosophic Duality}'', Florida: GLOBAL KNOWLEDGE - Publishing House 848 Brickell Ave Ste 950 Miami, Florida 33131 United States. ISBN: 978-1-59973-743-0 (http://fs.unm.edu/NeutrosophicDuality.pdf).  

\end{thebibliography}
\end{document}