1 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.
Kalpana, M.; Vijayalakshmi, D., 2018, On B-Coloring Of Central Graph Of Some Graphs, Communications Faculty Of Science University Of Ankara Series A1Mathematics And Statistics, 68, 1, pp. 1229-1239, 10.31801/cfsuasmas.516089.