On star coloring of degree splitting of join graphs

Abstract

A star coloring of a graph G is a proper vertex coloring in which every path on four vertices in G is not bicolored. The star chromatic number χs (G) of G is the least number of colors needed to star color G. In this paper, we have generalized the star chromatic number of degree splitting of join of any two graph G and H denoted by G + H, where G is a path graph and H is any simple graph. Also, we determine the star chromatic number for degree splitting of join of path graph G of order m with path Pn, complete graph Kn and cyclevgraph Cn.