Exact values for theb-chromatic number of a power completek-ary tree
Brice Effantin, Hamamache Kheddouci · Journal of Discrete Mathematical Sciences and Cryptography · 2005
Let G be a graph on vertices x1, x2,…, xn . 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 complete binary tree.