Geo Chromatic Number of a Graph

Beulah amli. S¹ , Robinson Chellathurai. S²

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.6 , pp.259-264, Dec-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.259264

Online published on Dec 31, 2018

Copyright © Beulah Samli. S, Robinson Chellathurai. S . 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 set S⊆V(G) is called a geodetic set if every vertex of G lies on a shortest u-v path for some u,v∈S, the minimum cardinality among all geodetic sets is called geodetic number and is denoted by g(G). A set C⊆V(G) is called a chromatic set if C contains all p vertices of different colors in G,the minimum cardinality among all chromatic sets is called chromatic number and is denoted by χ(G). The combination of a geodetic set and a chromatic set gives a new concept, which is called a geo chromatic set (briefly χ_gc-set) of G. A geo chromatic set S_c⊆V(G) is both a geodetic set and a chromatic set. The geo chromatic number χ_gc (G) of G is the minimum cardinality among all geo chromatic sets of G. We determined the geo chromatic numbers of certain standard graphs and bounds of the geo chromatic number is proved. Also we illustrated that for positive integers x,y,z with 2≤x

Key-Words / Index Term :
Geodetic number, chromatic number, Geo chromatic number

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