TOTAL COLORINGS OF CORE-SATELLITE, COCKTAIL PARTY AND MODULAR PRODUCT GRAPHS

TOTAL COLORINGS OF CORE-SATELLITE, COCKTAIL PARTY AND MODULAR PRODUCT GRAPHS

R. Vignesh, S. Mohan, J. Geetha, K. Somasundaram

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Abstract

A total coloring of a graph G is a combination of vertex and edge colorings of G. In other words, is an assignment of colors to the elements of the graph G such that no two adjacent elements (vertices and edges) receive a same color. The total chromatic number of a graph G, denoted by 00(G), is the minimum number of colors that suce in a total coloring. Total coloring conjecture (TCC) was proposed independently by Behzad and Vizing that for any graph G,
(G) + 1  00(G) 
(G) + 2, where
(G) is the maximum degree of G. In this paper, we prove TCC for Core Satellite graph, Cocktail Party graph, Modular product of paths and Shrikhande graph.

Keywords

Total coloring, Modular product graph, Core Satellite graph, Cocktail Party graph, Shrikhande graph.