The b-chromatic number of power graphs of complete caterpillars

Abstract Let G be a graph on vertices v 1, v 2,…, v n . 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 every color i admits a representant x adjacent to a vertex of each color j, 1≤j≠i≤k. In this paper, we give the exact value for the b-chromatic number of power graphs of a complete caterpillar.

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