On b-coloring of powers of hypercubes

A b-coloring of a graph G with k colors is a proper coloring of G using k colors in which each color class contains a color dominating vertex, that is, a vertex which has a neighbor in each of the other color classes. The largest positive integer k for which G has a b-coloring using k colors is the b-chromatic number b(G) of G. In this paper, we have obtained bounds for the b-chromatic number of powers of Qn, namely Qnp, for n≥5 and ⌊n2⌋