3度非对称的点传递图的性质

Some Properties of Trivalent Nonsymmetric Vertex-Transitive Graphs

设X为3度连通的简单无向图,X称为具有非平凡点稳定子群的非对称的点传递图,若X的全自同构群A在X的顶点集合上作用是传递的,而且X的任意顶点在A中的稳定子群在该点的邻域上的作用是非传递的、非平凡的.本文考察了这种图,我们给出了这类图的一些性质.

Let X be a simple undirected connected trivalent graph, X is said to be a nonsymmetric vertex-transitive graph with nontrivial vertex-stabilizer if the full automorphism group of X acts transitively on the vertex-set of X and the vertex-stabilizer in it of a vertex v has two orbits on the set of the three vertices adjacent to the vertex v. We prove some properties of these graphs.