The b-chromatic number of some power graphs
Brice Effantin, Hamamache Kheddouci · 2003
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 ≤ 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.