树和单圈图的点Co-PI指标的界

摘要

LetG=(V, E)be a connected graph.For e=uv∈E(G),let nu(e) be the number of vertices closer to u than to v, nv(e) be the number of vertices closer to v than to u.The vertex Co−PI index of G is defined as Co−PIv(G)= P|nu(e)−e=uv∈E(G) nv(e)|. In this paper, sharp upper and lower bounds on the vertex Co−PI index of trees and unicycilc graphs are reported. Moreover,the second,third,fourth minimum and the second maximum values of this index for unicyclic graphs are given.%令G=(V, E)是一个连通图。对于边e=uv∈E(G),令nu(e)为距u的距离比距v的距离近的点的个数, nv(e)为距v的距离比距u的距离近的点的个数。图G的点Co−PI指标定义为Co−PIv(G)= P|nu(e)−nv(e)|。在本文中,得e=uv∈E(G)到了树和单圈图的点Co−PI指标的上下界,并且给出了单圈图的点Co−PI指标的第二、第三、第四小和第二大值。