LAUSR

A Cayley graph Γ = Cay(G,S) is said to be core-free if G is core-free in some X for G ≤ X ≤AutΓ. A graph Γ is called s-regular if AutΓ acts regularly on its s-arcs. It is shown in this paper that if s ≤ 2, then there exist no core-free tetravalent s-regular Cayley graphs; and for s ≥ 3, every tetravalent s-regular Cayley graph is a normal cover of one of the three known core-free graphs. In particular, a characterization of tetravalent s-regular Cayley graphs is given.