Finite 1-Regular Cayley Graphs of Valency 5

Abstract EN

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.