三度边正则图的三个无限族  

Three Infinite Families of Cubic Edge-Regular Graphs

作　　者：路在平[1] 徐明曜[1] 

机构地区：[1]北京大学数学科学学院,北京100871

出　　处：《数学进展》2004年第1期115-120,共6页Advances in Mathematics（China）

基　　金：国家自然科学基金(19472024;10171006);山东省自然科学基金(Y2000A02).

摘　　要：图X称为边正则图,若X的自同构群Aut(X)在X的边集上的作用是正则的.本文考察了三度边正则图与四度Cayley图的关系,给出了一个由四度Cayley图构造三度边正则图的方法,并且构造了边正则图的三个无限族.A graph is said to be an edge-regular graph, if its full automorphism group Aut(X) acts regularly on its edge-set. In this paper, we investigate the relations between cubic edge-regular graphs and Cayley graphs of degree 4, and give a method to construct cubic edge-regular graphs by Cayley graphs of degree 4. We construct three infinite families of cubic edge regular graphs.

关 键 词：三度边正则图 自同构群 四度Cayley图 半对称图 二部图 

分 类 号：O157.5[理学—数学] O152[理学—基础数学]