A note on the automorphism groups of cubic Cayley graphs of finite simple groups

For a finite group G , a Cayley graph Γ = Cay ( G , S ) on G is said to be normal if G R ◃ Aut Γ . In this note, we prove that connected cubic non-symmetric Cayley graphs of the ten finite non-abelian simple groups G in the list of non-normal candidates given in [X.G. Fang, C.H. Li, J. Wang, M.Y. Xu, On cubic Cayley graphs of finite simple groups, Discrete Math. 244 (2002) 67–75] are normal.