## SOME RESULTS ON TOTAL CHROMATIC NUMBER OF A GRAPH

## *S.K. VAIDYA1, RAKHIMOL V.ISAAC*

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## Abstract

A total coloring of a graph is a proper coloring in which no two adjacent or incident graph elements receive the same color. The total chromatic number of a graph is the smallest positive integer for which the graph admits a total coloring. In this paper, we derive some results on total chromatic number of a graph.

## Keywords

total coloring, total chromatic number, splitting graph.