Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Dimension and Coloring alongside Domination in Neutrosophic Hypergraphs

Version 1 : Received: 24 December 2021 / Approved: 28 December 2021 / Online: 28 December 2021 (13:42:44 CET)

How to cite: Garrett, H. Dimension and Coloring alongside Domination in Neutrosophic Hypergraphs. Preprints 2021, 2021120448 (doi: 10.20944/preprints202112.0448.v1). Garrett, H. Dimension and Coloring alongside Domination in Neutrosophic Hypergraphs. Preprints 2021, 2021120448 (doi: 10.20944/preprints202112.0448.v1).

Abstract

New setting is introduced to study resolving number and chromatic number alongside dominating number. Different types of procedures including set, optimal set, and optimal number alongside study on the family of neutrosophic hypergraphs are proposed in this way, some results are obtained. General classes of neutrosophic hypergraphs are used to obtains these numbers and the representatives of the colors, dominating sets and resolving sets. Using colors to assign to the vertices of neutrosophic hypergraphs and characterizing resolving sets and dominating sets are applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different ways of study on neutrosophic hypergraphs to get new results about numbers and sets in the way that some numbers get understandable perspective. Family of neutrosophic hypergraphs are studied to investigate about the notions, dimension and coloring alongside domination in neutrosophic hypergraphs. In this way, sets of representatives of colors, resolving sets and dominating sets have key role. Optimal sets and optimal numbers have key points to get new results but in some cases, there are usages of sets and numbers instead of optimal ones. Simultaneously, three notions are applied into neutrosophic hypergraphs to get sensible results about their structures. Basic familiarities with neutrosophic hypergraphs theory and hypergraph theory are proposed for this article.

Keywords

Dimension; Coloring; Domination

Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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