Cubic Edge-transitive Graph Of Order 12p

Give a simple undirect regular graph X.If the graph Xhas no isolated vertice ,its full autmorphism group AutX acts transitively on arc set ,we say that X is arc-transtive or symmetric .If a subgroup G of AutX acts transitively on its vertex set (or edge set), we say that X is G—vertex-transtive (or G—edge-transtive) ,respectively.A regular G— edge-transtive but not G—vertex-transtive graph will be refered to as a G—semisymmetric graph .In the special case when G = AutX, we call a G—vertex-transtive graph, G—edge-transtive graph, G—semisymmetric graph X is vertex-transtive edge-transtive semisymmetric graph respectively In this paper we investigate the autmorphism graph AutX of the cubic semisymmetric graph of order 12p ,when p is primes.As a corollary ,we prove the nonexistance of cubic semisymmetric graph of order 12p,i.e.,for all edge-transitive cubic graph of 12p is symmetric.