The b-chromatic number of power graphs of complete caterpillars
Résumé
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 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.