Rainbow connection numbers of Cayley graphs

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.