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Ars Combinatoria

  • Research article

Vertex Distinguishing Edge- and Total-Colorings of Cartesian and other Product Graphs

Jean-Luc Baril1, Hamamache Kheddouci2, Olivier Togni3
1LE2I, UMR 5158 CNRS, Université de Bourgogne, BP 47870, 21078 Dijon cedex, France
2LIESP, Université-Claude Bernard Lyon, 843, Bd. du 11 novembre 1918, 68622 Villeurbanne Cedex France,
3 LE2I, UMR 5158 CNRS, Université de Bourgogne, BP 47870, 21078 Dijon cedex, France
  • Published: 31/10/2012

Abstract

This paper studies edge- and total-colorings of graphs in which (all or only adjacent) vertices are distinguished by their sets of colors. We provide bounds for the minimum number of colors needed for such colorings for the Cartesian product of graphs along with exact results for generalized hypercubes. We also present general bounds for the direct, strong and lexicographic products.

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Citation
Jean-Luc Baril, Hamamache Kheddouci, Olivier Togni. Vertex Distinguishing Edge- and Total-Colorings of Cartesian and other Product Graphs[J], Ars Combinatoria, Volume 107. 109-127. .