STAR-IN-COLORING OF COMPLETE BI-PARTITE GRAPHS, WHEEL GRAPHS AND PRISM GRAPHS

A k- coloring of a graph G=(V,E) is a mapping c:V (G)→{1,2,3,…} such that uv∈E(G)⇒c(u)≠c(v). In this paper, we have considered a complete bi-partite graph K_(m,n)for all m,n and proved that the star-in-chromatic number of K_(m,n) is either n + 1 if m ? n or m + 1 if n > m respectively. We have also found that the star-in-chromatic number of a wheel graph W_n has the lower bound and upper bound as 4 ? χ_si (W_n) ? 5. Further we have considered the prism graph Y_(n,m) and found that the star-in-chromatic number of the prism graph satisfies the relation 5 ?χ_si (Y_(n,m)) ? 6.