有限图的字典积的自同构群  

Automorphism Group of the Lexicographic Product of Finite Graphs

作　　者：王志俊 王登银 WANG Zhijun;WONG Dein(School of Mathematics,China University of Mining and Technology,Xuzhou,Jiangsu,221116,P.R.China)

机构地区：[1]中国矿业大学数学学院,徐州江苏221116

出　　处：《数学进展》2022年第6期996-1004,共9页Advances in Mathematics（China）

基　　金：Supported by NSFC(No.11971474)。

摘　　要：两个简单无向图G和H的字典积G∘H是一个以V(G)×V(H)为顶点集的图,两个顶点(i,h)和(j,k)在G∘H中邻接当且仅当i和j在G中邻接,或者i=j且h和k在H中邻接.图G∘H的自同构群Aut(G∘H)包含图G和图H的自同构群的圈积Aut(H)≀Aut(G)作为子群.Sabidussi给出了一个Aut(G∘H)=Aut(H)≀Aut(G)的充分必要条件.在此基础上,本文确定了任意两个有限图字典积的自同构群.The lexicographic product of two graphs G and H,denoted by G∘H,is defined to be the graph whose vertex set is V(G)×V(H),and two vertices(i,h),(j,k)are adjacent if and only if either i,j are adjacent in G or i=j and h,k are adjacent in H.The automorphism group Aut(G∘H)of G∘H contains the wreath product Aut(H)≀Aut(G)of Aut(H)by Aut(G)as a subgroup.Sabidussi gave a necessary and sufficient condition for Aut(G∘H)=Aut(H)≀Aut(G).Extending the result,we determine the automorphism group of the lexicographic product of arbitrary two finite graphs.

关 键 词：字典积图 图的自同构 半直积 圈积 

分 类 号：O157.5[理学—数学]