Publication

Abstract : Total Coloring of a graph is a variety of proper colorings in which no two adjacent vertices, edges incident on the same vertex, or an edge and its incident vertices receive the same color. The total chromatic number is the minimum number of colors required in any total coloring of a graph. The neighbor-sum distinguishing and equitable total chromatic numbers are generalizations of the total chromatic number. The computation of all three numbers is shown to be NP-hard. The circulant graphs are regular graphs with varying applications within and outside graph theory. They are the easiest examples of regular graphs that come to mind. They can be seen as the Cayley graphs on cyclic groups. In this paper, we have obtained better bounds for the total chromatic and equitable and neighbor- sum distinguishing total chromatic numbers of some classes of the circulant graphs.