Total Coloring of Splitting Graph of Path, Cycle and Star Graphs

Abstract

In 1965, the concept of total coloring was introduced by Behzad \cite{MB} and in 1967 he \cite{MG} came out new ideology that, the total chromatic number of complete graph and complete bi-partite graph. A total coloring of a graph $G$ is an assignment of colors to both the vertices and edges of $G,$ such that no two adjacent or incident vertices and edges of $G$ are assigned the same colors. In this paper, we have discussed the total coloring of splitting graph of Path, Cycle and Star graph. Also, we determine the total chromatic number of splitting graph of Path, Cycle and Star graphs.