## 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.