Star Coloring of Cartesian Product of Complete Bipartite Graphs, Double Star Graphs with Complete Bipartite Graphs

Abstract

Let K_m,n and D(K_1,r ,K_1,s) denotes a complete bipartite graph with m and n vertices and a double star graph on r and s vertices respectively. Let G₁□G₂ denotes the cartesian product of two graphs G₁ and G₂. In this paper, the star coloring of graphs such as K_m,n□K_m,n and D(K_1,r,K_1,s)□K_m,n have been studied and the star chromatic number χ_s is obtained for such graphs. It is proved that for given positive integers m, n, r, s ≥ 2 ,