Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Neutrosophic Chromatic Number Based on Connectedness

Version 1 : Received: 12 December 2021 / Approved: 14 December 2021 / Online: 14 December 2021 (11:14:50 CET)

How to cite: Garrett, H. Neutrosophic Chromatic Number Based on Connectedness. Preprints 2021, 2021120226. Garrett, H. Neutrosophic Chromatic Number Based on Connectedness. Preprints 2021, 2021120226.


New setting is introduced to study chromatic number. vital chromatic number and n-vital 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 vital edge from connectedness 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 vital chromatic number. This specific relation amid edges is necessary to compute both vital chromatic number concerning the number of representative in the set of representatives and n-vital chromatic number concerning neutrosophic cardinality of set of representatives. If two vertices have no vital 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.


Neutrosophic Connctedness; Neutrosophic Graphs; Chromatic Number


Computer Science and Mathematics, Applied Mathematics

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