Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer's Recognition as the Model in the Setting of (Neutrosophic) SuperHyperGraphs

Version 1 : Received: 14 January 2023 / Approved: 17 January 2023 / Online: 17 January 2023 (10:15:16 CET)

How to cite: Garrett, H. Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer's Recognition as the Model in the Setting of (Neutrosophic) SuperHyperGraphs. Preprints 2023, 2023010308. https://doi.org/10.20944/preprints202301.0308.v1 Garrett, H. Extreme SuperHyperClique as the Firm Scheme of Confrontation under Cancer's Recognition as the Model in the Setting of (Neutrosophic) SuperHyperGraphs. Preprints 2023, 2023010308. https://doi.org/10.20944/preprints202301.0308.v1

Abstract

In this research, new setting is introduced for assuming a SuperHyperGraph. Then a ``SuperHyperClique'' $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of SuperHyperVertices such that there's a SuperHyperVertex to have a SuperHyperEdge in common. Assume a SuperHyperGraph. Then an ``$\delta-$SuperHyperClique'' is a \underline{maximal} SuperHyperClique of SuperHyperVertices with \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta,~|S\cap N(s)| < |S\cap (V\setminus N(s))|+\delta.$ The first Expression, holds if $S$ is an ``$\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$\delta-$SuperHyperDefensive''; a``neutrosophic $\delta-$SuperHyperClique'' is a \underline{maximal} neutrosophic SuperHyperClique of SuperHyperVertices with \underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $s\in S:$ $~|S\cap N(s)|_{neutrosophic} > |S\cap (V\setminus N(s))|_{neutrosophic}+\delta,~ |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta.$ The first Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is a ``neutrosophic $\delta-$SuperHyperDefensive''. A basic familiarity with Extreme SuperHyperClique theory, SuperHyperGraphs, and Neutrosophic SuperHyperGraphs theory are proposed.

Keywords

(Neutrosophic) SuperHyperGraph; Extreme SuperHyperClique; Cancer's Extreme Recognition

Subject

Computer Science and Mathematics, Computer Vision and Graphics

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