2p^2阶3度点传递图

Cubic Vertex-transitive Graphs of Order 2p^2

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.本文证明了一个2p^2(p为素数)阶连通3度点传递图或者是Calyley图,或者同构于广义Petersen图P(p^2,t),这里t^2≡-1(modp^2).

A graph is said to be vertex-transitive, if its automorphism group is transitive on its vertices. In this paper, we prove that a connected cubic vertex-transitive graph of order 2p^2（p a prime） is either a Cayley graph or isomorphic to the generalized Petersen graph P（p^2, t）,where t^2 =-1（mod p^2）