Bipancyclic properties of Cayley graphs generated by transpositions

Cycle is one of the most fundamental graph classes. For a given graph, it is interesting to find cycles of various lengths as subgraphs in the graph. The Cayley graph Cay ( S n , S ) on the symmetric group has an important role for the study of Cayley graphs as interconnection networks. In this paper, we show that the Cayley graph generated by a transposition set is vertex-bipancyclic if and only if it is not the star graph. We also provide a necessary and sufficient condition for Cay ( S n , S ) to be edge-bipancyclic.