循环群的子群交图的一些性质  

Some Properties of Intersection Graphs of Subgroups of Cyclic Groups

作　　者：苏华东 朱灵 SU Hua-dong;ZHU Ling(School of Mathematics and Statistics!Nanning Normal University,Nanning 530299,China)

机构地区：[1]南宁师范大学数学与统计学院

出　　处：《南宁师范大学学报（自然科学版）》2019年第4期7-11,共5页Journal of Nanning Normal University：Natural Science Edition

基　　金：国家自然科学基金项目(11661013,11661014,11961050)

摘　　要：设G是一个群,群G的子群交图,记为Γ(G),是以G的非平凡子群为顶点,两个不同顶点H,K相连当且仅当H∩K≠{1}.一个图Γ的Wiener指标是指图Γ中任意两点的距离之和,记为W(Γ),即W(Γ)=∑x,y∈Γd(x,y).该文主要研究循环群的子群交图的自同构群和Wiener指标,得到了任意n阶循环群的子群交图的Wiener指标计算公式以及当循环群的阶的素因子不超过3个时,Γ(G)的自同构群的结构.Let G be a group.The intersection graph of G,denoted byΓ(G),is a graph whose vertices are non-trivial subgroups of G,and two distinct vertices H,K are adjacent if and only if H∩K≠1.LetΓbe a graph.The Wiener index of a graphΓis the sum of the distances of all pairs inΓ,denoted by W(Γ),i.e.,W(Γ)=∑x,y∈Γd(x,y).In this paper,we mainly study the automorphism x,y∈Γgroup and Wiener index of subgroup intersection graph of cyclic groups.We obtain the formulae of Wiener index ofΓ(G)for any cyclic group of order n and the structure of the automorphism group ofΓ(G)when the order of the cyclic group G has at most three prime divisors.

关 键 词：循环群 子群交图 自同构群 W iener指标 

分 类 号：O152[理学—数学] O157.5[理学—基础数学]