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  1. Home > Articles & Issues >
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  3. The b-chromatic numb ...
Article

The b-chromatic number of power graphs

Brice Effantin ORCID (1), Hamamache Kheddouci ORCID (1)
(1) Laboratoire Electronique, Informatique et Image [UMR6306]
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Imported on
March 26, 2015
Published on
January 1, 2003
Last modified on
March 31, 2025
Volume 6
vol. 6:1
DOI
10.46298/dmtcs.333
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https://about.hal.science/hal-authorisation-v1
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The b-chromatic number of power graphs

Brice Effantin ORCID (1), Hamamache Kheddouci ORCID (1)
(1) Laboratoire Electronique, Informatique et Image [UMR6306]
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 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.
Keywords
  • [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
  • coloring
  • b-chromatic number
  • power graph
  • path
  • cycle and complete binary tree.
  • cycle and complete binary tree
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