五角链的点PI指标(英文)

The Vertex PI Index of Pentagon Chains

图G的点PI指标指的是:取遍G中的每一条边,满足到这条边两个端点距离不相等的点的个数.为了得到五角链的点PI指标,把它的边分成三类并分别进行计算,可以得到五角链的点PI指标.利用PIv(G)=mn-∑S(e),给出二部图点PI指标的界:(n-1)n≤PIv(G)≤n.

The vertex Padmakar-Ivan（PIv） index of a graph G is introduced as the sum over all edges e=uv of G of the number of vertices which are not equidistant to the vertices u and v.In order to obtain the vertex PI index of Pentagon chains,we divide the edges of Pentagon chains into three categories and calculate respectively and then obtain the vertex PI index of Pentagon chains.By using PIv（G） = mn-∑S（e）,we establish the bounds for the vertex PI indices of bipartite graph：（n-1）nPIv（G） n.