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Erschienen in:
04.07.2016
Rainbow connection numbers of Cayley graphs
Erschienen in: Journal of Combinatorial Optimization | Ausgabe 1/2017
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Abstract
An edge colored graph is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number, rc-number for short, of a graph \({\varGamma }\), is the smallest number of colors that are needed in order to make \({\varGamma }\) rainbow connected. In this paper, we give a method to bound the rc-numbers of graphs with certain structural properties. Using this method, we investigate the rc-numbers of Cayley graphs, especially, those defined on abelian groups and on dihedral groups.