The b-chromatic number of some power graphs.

Let G be a graph on vertices v1,, v2,..., vn. The b-chromatic number of G 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, with 1 ≤ i &;le; k, has at least one representant xi adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. In this paper, we give the exact value for the b-chromatic number of power graphs of a path and we determine bounds for the b-chromatic number of power graphs of a cycle. [ABSTRACT FROM AUTHOR]