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Chromatic Number and Neutrosophic Chromatic Number
Version 1
: Received: 9 December 2021 / Approved: 10 December 2021 / Online: 10 December 2021 (13:08:38 CET)
How to cite: Garrett, H. Chromatic Number and Neutrosophic Chromatic Number. Preprints 2021, 2021120177. https://doi.org/10.20944/preprints202112.0177.v1 Garrett, H. Chromatic Number and Neutrosophic Chromatic Number. Preprints 2021, 2021120177. https://doi.org/10.20944/preprints202112.0177.v1
Abstract
New setting is introduced to study chromatic number. Neutrosophic chromatic number and 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 assigns to the vertices of neutrosophic graphs is applied. Some questions and problems are posed concerning ways to do further studies on this topic. Using strong edge 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 neutrosophic chromatic number. This specific relation amid edges is necessary to compute both chromatic number concerning the number of representative in the set of representatives and neutrosophic chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no strong 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 Strong; Neutrosophic Graphs; Chromatic Number
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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