Abstract
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⌋<p<n−1. Also we have found the exact value of the b-chromatic number of Qnp for n≥3, and p=⌊n2⌋ and p=n−1. In addition, we have determined the clique number of Qnp for n≥3 and the chromatic number of Qnp for n≥2 and ⌈2(n−1)3⌉≤p≤n−1.
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