树与它的公共邻点图之间的维纳指标的差（英文）

The Difference of the Wiener Index Between the Tree and Its Common Neighborhood Graph

一个连通图的维纳指标被定义为所有无序顶点对之间的距离和.如果G是一个简单图,那么con(G)是图G的公共邻点图,它们有相同的顶点集,并且在图G里如果两个顶点有一个公共邻点,则在图G的公共邻点图里这两个顶点是相邻的.该文得到了关于树和它的公共邻点图的维纳指标之间差的下界和上界.

The Wiener index of a connected graph is defined as the sum of distances between all unordered pairs of its vertices. If G is a simple graph,then con（G） the common neighborhood graph of G,has the same vertex set as G ,and two vertices of con（G） are adjacent if they have a common neighbor in G. In this paper,the lower bound and the upper bound of the difference of the Wiener index between the tree and its common neighborhood graph are obtained respectively.