Discrete Mathematics & Theoretical Computer Science
| 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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