pq阶亚循环群局部传递的图

Graphs on Metacyclic Group of Orderacts Locally-Transitively

所指的图是有限的、单的、无向的且无孤立点。如果图的自同构群分别在图的边集合和点集合上传递,分别称图是边传递的和点传递的。设G≤Aut(Γ),如果对于每个α∈V(Γ),Gα在Γ(α)上传递,则称Γ是G-局部传递图。主要利用边传递、点传递和局部传递的关系及陪集图的理论,获得了关于pq(p、q是素数,p>q)阶亚循环群局部传递的图的完全分类。获得的结果为:关于pq阶群局部传递的图或为弧传递图,或为二分的边传递图,或为一些边传递图的并。

All graphs are finite simple undirected graph with no isolated vertices in this paper, p and q are prime number. The graph Г is said to be G-vertex-transitive or edge-transitive if its automorphism group G acts transitively on the vertex set or edge set of Г. Gα is the stabilizer of α in automorphism group G for a α ∈ V（Г）, the set of vertices adjacent to α is called the neighborhood of α in F and denoted by Г（α）, F is said to be locally-transitive if Gα is transitive on Г（α）. In the paper we take advantanged of the relationships among vertex-transitive, edge-transitive and locallytransitive graphs and the theorey of the cosets graphs and completed the classification of graphs on which a metacylic group of orderacts locally transitively. The main results are： that the graphs which the group of order pq acts loclly transitively are arc-transitive graphs, edge-transitive graphs or the union of some edge-transitive graphs.