正则图的Balaban指标  

On Balaban Index of Regular Graphs

作　　者：邓波[1] 常彩冰 王守中[1] 安文俊[1] 

机构地区：[1]广东石油化工学院理学院,广东茂名525000

出　　处：《西南师范大学学报（自然科学版）》2016年第6期12-17,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11526059);广东石油化工学院引进人才项目(513085);创新培育项目(2015pyA044);软科学项目(2014065)

摘　　要：连通图的Balaban指标(也叫J指标)的定义是m1J(G)=m-n+2uv∑∈E(G)σG(u)σG(v)其中m,n分别是图G的边数和点数,σG(u)表示在G中从顶点u到其它各个顶点的距离之和.Balaban指标被广泛应用于各种QSAR和QSPR的研究.首先给出连通3-正则图的Balaban指标的一个上界.然后对KNOR M等人介绍的两类3-正则图,分别给出它们的Balaban指标计算公式和上界,改进了KNOR M等人的结果.The Balaban index（also called Jindex）of a connected graph Gis denoted asm1J（G）=m-n＋2uv∑∈E（G）σG（u）σG（v）where m,nare the edge number and vertex number of G,respectively,andσG（u）（resp.σG（v））denotes the total distance fromuto all the other verticals of G.The Balaban index has been widely used in various QSAR and QSPR studies.First,an upper bound forthe Balaban index of n-vertex r-regular graphs is presented.Then for two classes of cubic graphs introduced by KNOR M.et al.,a formula for the first kind of cubic graphs and an upper bound of J（G）for the other kind of cubic graphs are shown,respectively.And two problems proposed by KNOR M.et al.are solved.

关 键 词：Balaban指标 距离 3-正则图 上界 

分 类 号：O157.5[理学—数学]