Cubic -arc transitive Cayley graphs

This paper gives a characterization of connected cubic s -transitive Cayley graphs. It is shown that, for s ≥ 3 , every connected cubic s -transitive Cayley graph is a normal cover of one of 13 graphs: three 3-transitive graphs, four 4-transitive graphs and six 5-transitive graphs. Moreover, the argument in this paper also gives another proof for a well-known result which says that all connected cubic arc-transitive Cayley graphs of finite non-abelian simple groups are normal except two 5-transitive Cayley graphs of the alternating group A 47 .