A note on coset graphs

Coset graphs are a generalization of Cayley graphs. They arise in the construction of graphs and digraphs with transitive automorphism groups. Moreover, the consideration of coset graphs makes it possible to give an algebraic description of regular connected graphs of even degree. In this paper we consider the automorphism group of coset graphs with an edge set decomposed into oriented cycles and provide a characterization of subgroups of the automorphism group which preserve a given decomposition of the edge set. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim