有循环极大子群的素数幂阶群的作用是边传递的图(Ⅰ)

GRAPHS ON WHICH A GROUP OF PRIME POWER ORDER WITH A CYCLIC MAXIMAL SUBGROUP ACTS EDGE-TRANSITIVELY(***)

Γ是一个有限的、单的、无向的且无孤立点的图, G是Aut(Γ)的一个子群.如果G在Γ的边集合上传递,则称Γ是G-边传递图.我们完全分类了当G为一个有循环的极大子群的素数幂阶群时的G-边传递图.这扩展了Sander的结果.本文仅给出其中的一种情况,即当G同构于群时,所有的G-边传递图.结果为。

Let Γ be a finite simple undirected graph with no isolated vertices , G is a subgroup of Aut(Γ). The graph Γ is said to be G-edge transitive if G is transitive on the set of edges of Γ. We obtain a complete classification of G-edge transitive graphs , which G is a group of prime-power order with a cyclic maximal subgroup. This extend Sander's conclusion. In this paper, we only consider the case that G is isomorphic to group Then Γ is G-edge-transitive if and only if F is one of following graphs