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Bipancyclic properties of Cayley graphs generated by transpositions

2009; Elsevier BV; Volume: 310; Issue: 4 Linguagem: Inglês

10.1016/j.disc.2009.09.002

1872-681X

Yuuki Tanaka, Yosuke Kikuchi, Toru Araki, Yukio Shibata,

Advancements in Battery Materials

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.