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• W4313609312 abstract "In this research, new setting is introduced for new SuperHyperNotions, namely, an 1-failed SuperHyperForcing and Neutrosophic 1-failed SuperHyperForcing. Assume a SuperHyperGraph. Then an ``1-failed SuperHyperForcing'' $mathcal{Z}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex; a ``neutrosophic 1-failed SuperHyperForcing'' $mathcal{Z}_n(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a SuperHyperSet $S$ of black SuperHyperVertices (whereas SuperHyperVertices in $V(G) setminus S$ are colored white) such that $V(G)$ isn't turned black after finitely many applications of ``the color-change rule'': a white SuperHyperVertex is converted to a black SuperHyperVertex if it is the only white SuperHyperNeighbor of a black SuperHyperVertex. The additional condition is referred by ``1-'' about the usage of any black SuperHyperVertex only once to act on white SuperHyperVertex to be black SuperHyperVertex. Assume a SuperHyperGraph. Then an ``$delta-$1-failed SuperHyperForcing'' is a underline{maximal} 1-failed SuperHyperForcing of SuperHyperVertices with underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $sin S:$ $~|Scap N(s)| &gt; |Scap (Vsetminus N(s))|+delta,~|Scap N(s)| &lt; |Scap (Vsetminus N(s))|+delta.$ The first Expression, holds if $S$ is an ``$delta-$SuperHyperOffensive''. And the second Expression, holds if $S$ is an ``$delta-$SuperHyperDefensive''; a``neutrosophic $delta-$1-failed SuperHyperForcing'' is a underline{maximal} neutrosophic 1-failed SuperHyperForcing of SuperHyperVertices with underline{maximum} neutrosophic cardinality such that either of the following expressions hold for the neutrosophic cardinalities of SuperHyperNeighbors of $sin S:$ $~|Scap N(s)|_{neutrosophic} &gt; |Scap (Vsetminus N(s))|_{neutrosophic}+delta,~ |Scap N(s)|_{neutrosophic} &lt; |Scap (Vsetminus N(s))|_{neutrosophic}+delta.$ 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 SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed." @default.
• W4313609312 created "2023-01-07" @default.
• W4313609312 creator A5072323616 @default.
• W4313609312 date "2023-01-06" @default.
• W4313609312 modified "2023-09-27" @default.
• W4313609312 title "(Neutrosophic) 1-Failed SuperHyperForcing in Cancer’s Recognitions And (Neutrosophic) SuperHyperGraphs" @default.
• W4313609312 doi "https://doi.org/10.20944/preprints202301.0121.v1" @default.
• W4313609312 hasPublicationYear "2023" @default.
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