Brice Effantin ; Hamamache Kheddouci - The b-chromatic number of power graphs

dmtcs:333 - Discrete Mathematics & Theoretical Computer Science, January 1, 2003, Vol. 6 no. 1 - https://doi.org/10.46298/dmtcs.333
The b-chromatic number of power graphs

Authors: Brice Effantin ; Hamamache Kheddouci

    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.


    Volume: Vol. 6 no. 1
    Published on: January 1, 2003
    Imported on: March 26, 2015
    Keywords: cycle and complete binary tree,coloring,b-chromatic number,power graph,path,cycle and complete binary tree.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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