Discussiones Mathematicae Graph Theory 31(3) (2011) 547-557
doi: 10.7151/dmgt.1564

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ADJACENT VERTEX DISTINGUISHING EDGE COLORINGS OF THE DIRECT PRODUCT OF A REGULAR GRAPH BY A PATH OR A CYCLE

Laura Frigerio

Dip. di Elettronica e Informazione
Politecnico di Milano
Piazza L. da Vinci, 32, 20133 Milano, Italy
e-mail: lfrigerio@elet.polimi.it

Federico Lastaria and Norma Zagaglia Salvi

Dip. di Matematica
Politecnico di Milano
Piazza L. da Vinci 32, 20133 Milano, Italy
e-mail:federico.lastaria@polimi.it
e-mail:norma.zagaglia@polimi.it

Abstract

In this paper we investigate the minimum number of colors required for a proper edge coloring of a finite, undirected, regular graph G in which no two adjacent vertices are incident to edges colored with the same set of colors. In particular, we study this parameter in relation to the direct product of G by a path or a cycle.

Keywords: chromatic index, adjacent vertex distinguishing edge coloring, direct product, matching.

2010 Mathematics Subject Classification: 05C15, 05C38.

References

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Received 11 December 2008
Revised 2 March 2010
Accepted 8 August 2010