Basic Notions on (Neutrosophic) SuperHyperForcing And (Neutrosophic) SuperHyperModeling in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs
Authors: Garrett Henry 
Published: January 2023

In this research, assume a SuperHyperGraph. Then a &ldquo;SuperHyperForcing&rdquo; Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of &ldquo;the color-change rule&rdquo;: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a &ldquo;neutrosophic SuperHyperForcing&rdquo; Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of &ldquo;the color-change rule&rdquo;: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then a &ldquo;SuperHyperForcing&rdquo; Z(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of &ldquo;the color-change rule&rdquo;: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex; a &ldquo;neutrosophic SuperHyperForcing&rdquo; Zn(NSHG) for a neutrosophic SuperHyperGraph NSHG : (V,E) is the minimum neutrosophic cardinality of a SuperHyperSet S of black SuperHyperVertices (whereas SuperHyperVertices in V (G) \ S are colored white) such that V (G) is turned black after finitely many applications of &ldquo;the color-change rule&rdquo;: a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. Assume a SuperHyperGraph. Then an &ldquo;&delta;&minus;SuperHyperForcing&rdquo; is a minimal SuperHyperForcing of SuperHyperVertices with minimum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of s &isin; S : |S&cap;N(s)|&gt;|S&cap;(V \N(s))|+&delta;, |S&cap;N(s)|&lt;|S&cap;(V \N(s))|+&delta;.Thefirst Expression, holds if S is an &ldquo;&delta;&minus;SuperHyperOffensive&rdquo;. And the second Expression, holds if S is an &ldquo;&delta;&minus;SuperHyperDefensive&rdquo;; a&ldquo;neutrosophic &delta;&minus;SuperHyperForcing&rdquo; is a minimal neutrosophic SuperHyperForcing of SuperHyperVertices with minimum neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of s &isin; S : |S &cap; N(s)|neutrosophic &gt; |S &cap; (V \ N (s))|neutrosophic + &delta;, |S &cap; N (s)|neutrosophic &lt; |S &cap; (V \ N (s))|neutrosophic + &delta;. The first Expression, holds if S is a &ldquo;neutrosophic &delta;&minus;SuperHyperOffensive&rdquo;. And the second Expression, holds if S is a &ldquo;neutrosophic &delta;&minus;SuperHyperDefensive&rdquo;. It&rsquo;s useful to define &ldquo;neutrosophic&rdquo; version of SuperHyperForcing. Since there&rsquo;s more ways to get type-results to make SuperHyperForcing more understandable. For the sake of having neutrosophic SuperHyperForcing, there&rsquo;s a need to &ldquo;redefine&rdquo; the notion of &ldquo;SuperHyperForcing&rdquo;. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there&rsquo;s the usage of the position of labels to assign to the values. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.