# 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 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.
If your browser does not display the abstract correctly (because of the different mathematical symbols) you can look it up in the PostScript or PDF files. |

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. |

ps.gz-source: | dm060104.ps.gz (39 K) |

ps-source: | dm060104.ps (150 K) |

pdf-source: | dm060104.pdf (115 K) |

The first *source* gives you the `gzipped' PostScript, the second the plain
PostScript and the third the format for the Adobe accrobat
reader. Depending on the installation of your web browser, at least
one of these should (after some amount of time) pop up a window for
you that shows the full article. If this is not the case, you should
contact your system administrator to install your browser correctly.

Due to limitations of your local software, the two formats may show up differently on your screen. If eg you use xpdf to visualize pdf, some of the graphics in the file may not come across. On the other hand, pdf has a capacity of giving links to sections, bibliography and external references that will not appear with PostScript.

Automatically produced on Wed May 7 21:47:52 CEST 2003 by falk