Finite 1-Regular Cayley Graphs of Valency 5 - Li, Jing Jian; Lou, Ben Gong; Zhang, Xiao Jun (International Journal of Combinatorics, 2013)
Let Γ=Cay(G,S) and G≤X≤AutΓ. We say Γ is (X,1)-regular Cayley graph if X acts regularly on its arcs. Γ is said to be core-free if G is core-free in some X≤Aut(Cay(G,S)). In this paper, we prove that if an (X,1)-regular Cayley graph of valency 5 is not normal or binormal, then it is the normal cover of one of two core-free ones up to isomorphism. In particular, there are no core-free 1-regular Cayley graphs of valency 5.