Some bounds for the b-chromatic number of a graph Original Research Article

In this paper we study the b-chromatic number of a graph G. This number is defined as the maximum number k of colors that can be used to color the vertices of G, such that we obtain a proper coloring and each color i has at least one representant xi adjacent to a vertex of every color j, 1⩽j≠i⩽k. The main result is the determination of two lower bounds for the b-chromatic number of the cartesian product of two graphs.