Total Chromatic Number of Comb Product of Arrow Graph with Certain Graphs

Abstract

         The total chromatic number of a graph  is defined to be the minimum number of colors needed to color the vertices and edges of a graph in such a way that no two adjacent vertices, no two adjacent edges and no edge and its end its end vertices given the same color. In this paper, we have obtained the total coloring and total chromatic number of comb product of arrow graph with path, star, fan and cycle.