交错群A_5的4度连通对称图的分类  

A CLASSIFICATION OF 4-VALENT SYMMETRIC GRAPHS OF SIMPLE GROUP A_5

作　　者：郭大昌[1] 

机构地区：[1]广东工业大学数理系,广州510643

出　　处：《广东机械学院学报》1997年第1期64-69,共6页Industrial Engineering Journal

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.

关 键 词：群 对称图 点传递图 交错群 图论 

分 类 号：O157.5[理学—数学]