Cubic Edge-transitive Graph Of Order 16p～2

Give a simple undirect regular graph X. If the graph X has no isolated vertices,and its full automorphism group AntX acts transitively on its arc sets, we say that X is arc-transtive or symmetric graph. 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 referred 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 cubic semisymmetric graphs of order 16p~2 by their automorphism groups AutX,when p is a prime. As a result, we prove the nonexistance of cubic semisymmetric graphs of order 16p~2, i.e., any edge-transitive cubic graph of 16p~2 is symmetric.