A Study on Geo Chromatic Number of Some Graph Families

U. Mary¹ , R. Joseph Paul²

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.5 , pp.1-6, Oct-2022

Online published on Oct 31, 2022

Copyright © U. Mary, R. Joseph Paul . 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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Abstract :
A proper coloring of a graph is that the allocate colors to the vertices of a graph in order that no two neighboring vertices have a similar color. The chromatic number is that the smallest number of colors needed to color G. The least cardinality among all the geodetic sets is known as geodetic number and is termed by g (G) and also the set C V (G) is termed as chromatic set if C contains all k-vertices of various colors in G, the least cardinality among all chromatic set is termed chromatic number and is denoted as . The synthesis of these concepts is termed Geo chromatic number . In this paper, we discuss about the Geo chromatic number of a Barbell graph, Helm graph, Gear Graph, Tadpole graph, Pan Graph, Lollipop graph, Bistar graph, Tristar graph, Web graph and Friendship graph are shown.

Key-Words / Index Term :
Geodetic Number, Chromatic Number, Geo Chromatic Number

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