Neut. SuperHyperEdges

Abstract

In this book, there are two chapters “Initial Notions” and “Modified Notions” about some researches on SuperHyperGraph and neutrosophic SuperHyper- Graph based on neutrosophic SuperHyperEdges.

In the first chapter, based on neutrosophic SuperHyperEdge (NSHE) in neutrosophic SuperHyperGraph (NSHG), I introduce some neutrosophic no- tions. I define different types of neutrosophic SuperHyperEdge (NSHE), neutrosophic SuperHyperPath (NSHP), stable (k-number/dual/perfect/total) (SuperHyperResolving/SuperHyperDominating) number, connected (k- number/dual/perfect/total) (SuperHyperResolving/SuperHyperDominating) number, (-/stable/connected) (-/dual/total) perfect (SuperHyperResolving/Su- perHyperDominating) set, general forms of neutrosophic SuperHyperGraph (NSHG), p neutrosophic SuperHyperGraph (pNSHG), x neutrosophic SuperHy- perGraph (xNSHG), and t-norm neutrosophic SuperHyperGraph (tNSHG) with related characterizations. Also, I formalize restricted status of neutrosophic classes of neutrosophic SuperHyperGraph (NSHG). Basic neutrosophic notions concerning hugely diverse types of neutrosophic SuperHyperDominating and hugely diverse types of neutrosophic SuperHyperResolving in neutrosophic SuperHyperGraph are introduced. Hugely diverse types of general forms of neutrosophic SuperHyperGraph are discussed. Hugely diverse types of neutrosophic SuperHyperEdges are defined. Different neutrosophic notions are assigned to neutrosophic SuperHyperPaths. Restricted status of neutrosophic classes of neutrosophic SuperHyperGraphs are presented. Different types of neutrosophic strengths and cardinalities are used. Further directions about some types of neutrosophic SuperHyperGraphs are summarized.

In the second chapter, in this research article, the notions of SuperHyperDom- inating and SuperHyperResolving are defined in the setting of neutrosophic SuperHyperGraphs. Some ideas are introduced on both notions of SuperHy- perDominating and SuperHyperResolving, simultaneously and as the same with each other. Some neutrosophic SuperHyperClasses are defined based on the notion, SuperHyperResolving. The terms of duality, totality, perfectness, connectedness, and stable, are added to basic framework and initial notions, SuperHyperDominating and SuperHyperResolving but the concentration is on the “perfectness” to figure out what’s going on when for all targeted SuperHyperVertices, there’s only one SuperHyperVertex in the intended set. There are some instances and some clarifications to make sense about what’s

i

Abstract

happened and what’s done in the starting definitions. The key point is about the minimum sets. There are some questions and some problems to be taken as some avenues to pursue this study and this research. A basic familiarity with SuperHyperGraph theory and neutrosophic SuperHyperGraph theory are proposed.

The following references are cited by chapters.

[Ref1] Henry Garrett, “Basic Neutrosophic Notions Concerning Neutrosophic SuperHyperDominating and Neutrosophic SuperHyperResolving in Neutrosophic SuperHyperGraph”, ResearchGate 2022 (doi: 10.13140/RG.2.2.29173.86244).

[Ref2] Henry Garrett, “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).

Some studies and researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 1850 readers in Scribd. It’s titled “Beyond Neutro- sophic 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.

[Ref] Henry Garrett, (2022). “Beyond Neutrosophic Graphs”, Ohio: E-publishing: Educational Publisher 1091 West 1st Ave Grand- view Heights, Ohio 43212 United States. ISBN: 978-1-59973-725-6

(http://fs.unm.edu/BeyondNeutrosophicGraphs.pdf).

Also, some studies and researches about neutrosophic graphs, are proposed as book in the following by Henry Garrett (2022) which is indexed by Google Scholar and has more than 2534 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.

[Ref] Henry Garrett, (2022). “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).

In this book, there are two chapters “Initial Notions” and “Modified Notions” about some researches on SuperHyperGraph and neutrosophic SuperHyperGraph based on neutrosophic SuperHyperEdges.

ii