b-Coloring of Some Powers of Hypercubes

The b-chromatic number b(G) of a graph G is the maximum k for which G has a proper vertex coloring using k colors such that each color class contains at least one vertex adjacent to a vertex of every other color classes. In this paper, we mainly investigate on one of the open problems given in [1]. As a consequence, we obtain an upper bound for the b-chromatic number of some powers of hypercube. This turns out to be the improvement of the existing bounds.