A Note On Equitable Total Coloring of Middle and Total Graph of Some Graphs

G. Jayaraman 1, D. Muthuramakrishnan2
1Department of Mathematics, Vels Institute of Science Technology and Advanced Studies, Chennai, India
2Department of Mathematics, National College(Autonomous), Trichy, India

Abstract

Among the varius coloring of graphs, the concept of equitable total coloring of graph \(G\) is the coloring of all its vertices and edges in which the number of elements in any two color classes differ by atmost one. The minimum number of colors required is called its equitable total chromatic number. In this paper, we obtained an equitable total chromatic number of middle graph of path, middle graph of cycle, total graph of path and total graph of cycle.

Keywords: Middle graph, Total graph, Equitable total coloring and Equitable total chromatic number.