Tetravalent edge-transitive cayley graphs of PGL (2, p)

Let Γ = Cay(G, S), R(G) be the right regular representation of G. The graph Γ is called normal with respect to G, if R(G) is normal in the full automorphism group Aut(Γ) of Γ. Γ is called a bi-normal with respect to G if R(G) is not normal in Aut(Γ), but R(G) contains a subgroup of index 2 which is normal in Aut(Γ). In this paper, we prove that connected tetravalent edge-transitive Cayley graphs on PGL(2, p) are either normal or bi-normal when p ≠ 11 is a prime.