On b-coloring of cartesian product of graphs.
Ramin Javadi, Behnaz Omoomi · Ars Combinatoria · 2012
A b-coloring of a graph G by k colors is a proper k-coloring of the vertices of G such that in each color class there exists a vertex having neighbors in all the other k−1 color classes. The b-chromatic number φ(G) of a graph G is the maximum k for which G has a b-coloring by k colors. This concept was introduced by R.W. Irving and D.F. Manlove in 1999. In this paper we study the b-chromatic numbers of the cartesian products of paths and cycles with complete graphs and the cartesian product of two complete graphs.