On star coloring of tensor product of graphs

Abstract

A star coloring of a graph $G$ is a proper coloring of the vertices of $G$ in which every path on four vertices in $G$ uses at least three distinct colors. The star chromatic number of $G$, denoted by $\chi_{s}(G)$ is the smallest integer $k$ for which $G$ admits a star coloring with $k$ colors. In this paper, we have obtained the star chromatic number of path with star graph and ladder graph. Also we obtained the star chromatic number of star graph with star graph and complete graph.