Discrete Mathematics & Theoretical Computer Science, Vol 6, No 1 (2003)

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DMTCS vol 6 no 1 (2003), pp. 45-54

Discrete Mathematics & Theoretical Computer Science


Volume 6 n° 1 (2003), pp. 45-54

author:Brice Effantin and Hamamache Kheddouci
title:The b-chromatic number of power graphs
keywords:coloring, b-chromatic number, power graph, path, cycle and complete binary tree.
abstract: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 xi 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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reference: Brice Effantin and Hamamache Kheddouci (2003), The b-chromatic number of power graphs, Discrete Mathematics and Theoretical Computer Science 6, pp. 45-54
bibtex:For a corresponding BibTeX entry, please consider our BibTeX-file.
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Automatically produced on Wed May 7 21:47:52 CEST 2003 by falk