内蒙古师范大学学报(自然科学汉文版)
內矇古師範大學學報(自然科學漢文版)
내몽고사범대학학보(자연과학한문판)
Journal of Inner Mongolia Normal University (Natural Science Edition)
2015年
5期
581-585
,共5页
点PI指标%Szeged指标%图的 cluster乘积%图的 corona乘积
點PI指標%Szeged指標%圖的 cluster乘積%圖的 corona乘積
점PI지표%Szeged지표%도적 cluster승적%도적 corona승적
Vertex PI index%Szeged index%cluster product%corona product
连通图 G 的点 PI 和 Szeged 指标分别定义为 PIv(G)=∑[nu (e G)+nv (e G)]和e=uv∈E(G) Sz(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, e=uv∈E(G) 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G°H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G°H的点PI和Szeged指标的精确表达式。
連通圖 G 的點 PI 和 Szeged 指標分彆定義為 PIv(G)=∑[nu (e G)+nv (e G)]和e=uv∈E(G) Sz(G)=∑nu(e G)nv(e G),其中nu(e G)錶示圖G中到點u 的距離小于到點v 的距離的點的箇數, e=uv∈E(G) nv (e G)錶示圖G中到點v的距離小于到點u的距離的點的箇數。設G{H}和G°H分彆錶示兩箇圖G和H 的cluster乘積和corona乘積。利用因子圖的相關拓撲指標分彆給齣計算G{H}和G°H的點PI和Szeged指標的精確錶達式。
련통도 G 적점 PI 화 Szeged 지표분별정의위 PIv(G)=∑[nu (e G)+nv (e G)]화e=uv∈E(G) Sz(G)=∑nu(e G)nv(e G),기중nu(e G)표시도G중도점u 적거리소우도점v 적거리적점적개수, e=uv∈E(G) nv (e G)표시도G중도점v적거리소우도점u적거리적점적개수。설G{H}화G°H분별표시량개도G화H 적cluster승적화corona승적。이용인자도적상관탁복지표분별급출계산G{H}화G°H적점PI화Szeged지표적정학표체식。
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.