On pentavalent 1-transitive Cayley graphs

A Cayley graph Γ=Cay(G,S) is said to be core-free if GG is core-free in some X≤AutΓ. In this paper, a characterization of connected core-free pentavalent 1-transitive Cayley graphs is given. Moreover, the argument in this paper also gives another proof for a result in Zhou and Feng (2010) which says that all connected pentavalent 1-transitive Cayley graphs of finite non-abelian simple groups are normal.