The b-chromatic number of power graphs

Brice Effantin (1) , Hamamache Kheddouci (1)

1 Le2i - Laboratoire Electronique, Informatique et Image [UMR6306]

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.

Mots clés: coloring; b-chromatic number; power graph; path; cycle and complete binary tree.; cycle and complete binary tree

Domaines: Mathématique discrète [cs.DM]

Brice Effantin, Hamamache Kheddouci. The b-chromatic number of power graphs. Discrete Mathematics and Theoretical Computer Science, 2003, Vol. 6 no. 1 (1), pp.45-54. ⟨10.46298/dmtcs.333⟩. ⟨hal-00958987⟩