Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Different Types of Neutrosophic Chromatic Number

Version 1 : Received: 20 December 2021 / Approved: 21 December 2021 / Online: 21 December 2021 (13:33:11 CET)

How to cite: Garrett, H. Different Types of Neutrosophic Chromatic Number. Preprints 2021, 2021120335 (doi: 10.20944/preprints202112.0335.v1). Garrett, H. Different Types of Neutrosophic Chromatic Number. Preprints 2021, 2021120335 (doi: 10.20944/preprints202112.0335.v1).

Abstract

New setting is introduced to study chromatic number. Different types of chromatic numbers and neutrosophic chromatic number are proposed in this way, some results are obtained. Classes of neutrosophic graphs are used to obtains these numbers and the representatives of the colors. Using colors to assign to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using different types of edges from connectedness in same neutrosophic graphs and in modified neutrosophic graphs to define the relation amid vertices which implies having different colors amid them and as consequences, choosing one vertex as a representative of each color to use them in a set of representatives and finally, using neutrosophic cardinality of this set to compute types of chromatic numbers. This specific relation amid edges is necessary to compute both types of chromatic number concerning the number of representative in the set of representatives and types of neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no intended edge, then they can be assigned to same color even they’ve common edge. Basic familiarities with neutrosophic graph theory and graph theory are proposed for this article.

Keywords

Neutrosophic Connctedness; Neutrosophic Graphs; Chromatic Number

Subject

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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