Cluster乘积图的点PI和Szeged指标  

The Vertex PI and Szeged Indices of Cluster Product Graphs

作　　者：罗朝阳[1,2] 

机构地区：[1]昌吉学院数学系,新疆昌吉831100 [2]山东大学数学学院,山东济南250100

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2015年第5期581-585,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：新疆维吾尔自治区自然科学基金资助项目(201442137-3);新疆维吾尔自治区高校科研计划重点项目(XJEDU2014I046)

摘　　要：连通图G的点PI和Szeged指标分别定义为PIv(G)=∑e=uv∈E(G)[nu(e G)+nv(e G)]和Sz(G)=∑e=uv∈E(G)nu(e G)nv(e G),其中nu(e G)表示图G中到点u的距离小于到点v的距离的点的个数,nv(e G)表示图G中到点v的距离小于到点u的距离的点的个数.设G{H}和GoH分别表示两个图G和H的cluster乘积和corona乘积.利用因子图的相关拓扑指标分别给出计算G{H}和GoH的点PI和Szeged指标的精确表达式.Let G be a connected graph.The vertex PI and Szeged indices of graph G are defined as PI v （G）= ∑[nu（e G）＋nv（e G）]and Sz（G）= ∑nu（e G）nv（e G）,where nu（e G）denotes the e=uv∈E（G） e=uv∈E（G） number of vertices of G whose distance to the vertex u is smaller than the distance to the vertex v,and nv（e G）denotes the number of vertices of G whose distance to the vertex v is smaller than the distance to the vertex u.Let G{H}and G°H be the cluster and corona products of two graphs G and H.In this paper, the explicit formulas for the vertex PI and Szeged indices of G{H}and G°H by means of some invariants of the factors are presented,respectively.

关 键 词：点PI指标 Szeged指标 图的cluster乘积 图的corona乘积 

分 类 号：O157.6[理学—数学]