6533b824fe1ef96bd12813fa
RESEARCH PRODUCT
The b-chromatic number of power graphs
Hamamache KheddouciBrice Effantinsubject
b-chromatic numberGeneral Computer Science[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]power graphTheoretical Computer ScienceCombinatoricsComputer Science::Discrete MathematicsDiscrete Mathematics and CombinatoricsChromatic scaleGraph coloringcoloringMathematicscycle and complete binary treeMathematics::CombinatoricsBinary treelcsh:Mathematicscycle and complete binary tree.path[ INFO.INFO-DM ] Computer Science [cs]/Discrete Mathematics [cs.DM]Complete coloringlcsh:QA1-939Vertex (geometry)Brooks' theorem[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Edge coloringFractional coloringdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2003-06-01 | Discrete Mathematics & Theoretical Computer Science |