Vertex-transitive graphs: Symmetric graphs of prime valency
Vertex-transitive graphs: Symmetric graphs of prime valency
复制标题
DOI：
10.1002/jgt.3190080107
复制
发表时间：
1984-03
期刊：
影响因子：
--
通讯作者：
P. Lorimer
中科院分区：
文献类型：
--
作者：
P. Lorimer
设G是对称作用在图Σ上的群，G1是对称作用在Σ上的群中G极小的子群，G2是G1的正规子群中除固定Σ的一个顶点的1外不含其他成员的极小G的子群.本文最精确的结果是：如果Σ有素数p，则Σ是一个二部图，或者G2正则作用在Σ上，或者G1|G2是一个对称作用于一个p度图的简单群，该图可以由Σ构造并且不比Σ有更多的顶点。也包括了建立这样的结果所必需的关于点传递群的结果。
Let G be a group acting symmetrically on a graph Σ, let G1 be a subgroup of G minimal among those that act symmetrically on Σ, and let G2 be a subgroup of G1 maximal among those normal subgroups of G1 which contain no member except 1 which fixes a vertex of Σ. The most precise result of this paper is that if Σ has prime valency p, then either Σ is a bipartite graph or G2 acts regularly on Σ or G1 | G2 is a simple group which acts symmetrically on a graph of valency p which can be constructed from Σ and does not have more vertices than Σ. The results on vertex-transitive groups necessary to establish results like this are also included.