Graphs on Which a Group of Prime Power Order with a Cyclic MaximalSubgroup Acts Edge-Transitively (II)
有循环极大子群的素数幂阶群的作用是边传递的图(II)

Let ${\it \Gamma}$ be a finite simple undirected graph with no isolated vertices, $G$ is a subgroup of Aut$({\it \Gamma})$. The graph ${\it \Gamma}$ is said to be $G$-edge transitive if $G$ is transitive on the set of edges of ${\it \Gamma}$. We obtain a complete classification of $G$-edge transitive graphs, when $G$ is a group of prime-power order with a cyclic maximal subgroup. This extends Sander's conclusion. Then ${\it \Gamma}$ is $G$-edge-transitive if and only if ${\it \Gamma}$ is one of following graphs:1)\ $p^mK_{1,p^{n-1-m}}$, $0\leq m\leq n-1$;2)\ $p^mK_{1,p^{n-m}}$, $0\leq m\leq n$;3)\ $p^mK_{p,p^{n-m-1}}$, $0\leq m\leq n-2$;4)\ $p^{n-m}C_{p^m}$, $p^m\geq 3,\ m