4p阶3度点传递图

CUBIC VERTEX-TRANSITIVE GRAPHS OF ORDER 4p

一个图称为点传递图,如果它的全自同构群在它的顶点集合上作用传递.证明了一个4p(p为素数)阶连通3度点传递图或者是Cayley图,或者同构于下列之一:广义Petersen图P(10,2),正十二面体,Coxeter图,或广义Petersen图P(2p,k),这里k^2=-1(mod 2p).

A graph is said to be vertex-transitive, if its automorphism group is transitive on its vertices. In this paper, it is proven that a connected cubic vertex-transitive graph of order 4p（p a prime） is either a Cayley graph or isomorphic to one of the following： the generalized Petersen graph P（10, 2）, the Dodecahedron, the Coxeter graph, or the generalized Petersen graph P（2p, k） where k^=-1mod 2p）.