Geodesic
The b-chromatic number of power graphs
Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 1.

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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. 
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Effantin, Brice; Kheddouci, Hamamache. The b-chromatic number of power graphs. Discrete mathematics & theoretical computer science, Tome 6 (2003-2004) no. 1. doi : 10.46298/dmtcs.333. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.333/

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