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The b-chromatic number of power graphs

Abstract : The b-chromatic number of a graph 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≤ k, has at least one representant x_i adjacent to a vertex of every color j, 1 ≤ j ≠ i ≤ k. In this paper, we discuss the b-chromatic number of some power graphs. We give the exact value of the b-chromatic number of power paths and power complete binary trees, and we bound the b-chromatic number of power cycles.
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Brice Effantin, Hamamache Kheddouci. The b-chromatic number of power graphs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2003, Vol. 6 no. 1 (1), pp.45-54. ⟨10.46298/dmtcs.333⟩. ⟨hal-00958987⟩



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