摘要
一个图Г称为G-对称的(symmetric).如果其同构群Aut(r)的一个子群G在图r的有向孤集(set of ordered pairs of adjacent vertices)上的作用是传递的(transitive).本文主要结果是:设图Г是4度对称图.全自同构群Aut(r)=A_5,则图r是且仅是如下图之一:(1)Г是15个点的完全图K_5的三维覆盖(3-fold cover)图.(2)Г是完全图K_5.
Let be a simple undirected graph and G a subgroup of Aut is said to be G-symmetric if G acts transitively on the set of ordered adjacent pairs of vertices of ; In this paper a complete classification for 4-valence symmetric graphs of A5 is given:Let Aut() be full automorphism group of and the valence of symmetric graph is 4. If Aut() = A5 then is one of the following graph:(I) is complete graph K5;(II) is 3-fold covering graph of K5.
出处
《广东机械学院学报》
1997年第1期64-69,共6页
Industrial Engineering Journal
关键词
群
对称图
点传递图
交错群
图论
group
symmetric graph
vertex-transitive graph
