一类边传递图

A Class of Edge Transitive Graphs

令G=〈α,β|αn=β2=1,αβ=αr〉,r2≡1(mod n),是图Γ的一个自同构群。目的是研究关于G-边传递图的性质,运用置换群和代数图论的相关理论,获得了这类图的完全分类,它们是一些互不相交的圈和完全二部图的并。

Let F be a finite simple undirected graph with no isolated vertices,G=（α,β｜α^n=β^2=1,α^β=α^r）,r＆^2≡1（modn） ,is a subgroup of Aut（F）. It is the purpose studying the properties and classification of G-edge-tran- sitive graphs in this paper. Using the theory, of permutation groups and algebraic graph theory, we obtain a completely classification of G-edge-transitive graphs. It is shown that they are the union of some circles which are mutual disjoint and completely two-Dart graph.