The distinguishing chromatic number of Cartesian products of two complete graphs

A labeling of a graph G is distinguishing if it is only preserved by the trivial automorphism of G. The distinguishing chromatic number of G is the smallest integer k such that G has a distinguishing labeling that is at the same time a proper vertex coloring. The distinguishing chromatic number of the Cartesian product Kk Kn is determined for all k and n. In most of the cases it is equal to the chromatic number, thus answering a question of Choi, Hartke and Kaul whether there are some other graphs for which this equality holds. Key words: distinguishing chromatic number; graph automorphism; Cartesian product of graphs AMS subject classification (2000): 05C15, 05C25

• Type: Journal
• Year: 2010
• Where: DM
• Authors: Janja Jerebic, Sandi Klavzar
• Keywords: Cartesian Product, Chromatic Number, DM 2010, Trivial Automorphism