On Star Coloring of Degree Splitting of Cartesian Product Graphs

Abstract

A star coloring of a graph G is a proper vertex coloring with the condition that no path on four vertices in G can be labelled by two colors. The star chromatic number χs (G) of G is the least number of colors that is required to star color G. In this paper, we determine the star chromatic number of the degree splitting graph of the Cartesian product of any two simple graphs G and H denoted by GH and also we portray the star chromatic number for the degree splitting graph of the Cartesian product of prism graphs, toroidal graphs and grid graphs.

Key words and phrases. Star coloring, Cartesian product, degree splitting.

2010 Mathematics Subject Classification. 05C15, 05C75