.8 P 2 Order 3 Degrees Side-transitive Graphs

Given a simple undirect regular graph X, If the graph X has 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 reffered to as a G-semisymmetric graph. In the special case when G = AutX, we call a G-vertex-transtive graph, G-edge-transtive graph and G-semisymmetric graph X is vertex-transtive , edge-transtive and semisymmetric respectively. In this paper, the influence of edge-transtivity on vertex-transtivity and semi-symmetry is invesigated. we study edge-transitive cubic graphs of order 8p2 in detail. As a result , it is proved that edge-transitive cubic graphs of 8p2 is symmetric, i. e. , there are no semisymmetric cubic graphs of order 8p2.