具有次大Wiener指数的单圈图

Unicyclic Graphs with the Second Largest Wiener Index

设G=(V,E)是一个简单连通图,V和E分别为G的顶点集和边集.研究了单圈图的Wiener指数,利用单圈图的Wiener指数的计算公式,刻划了具有次大Wiener指数的单圈图的特征.

Let G = （V, E） be a simple connected graph with vertex set V and edge set E. The Wiener index W（G） of G is the sum of distances between all pairs of vertices in G, i.e., W（G）= ∑dG（u,v）{u,v}belong to G Where dG（u,v）is the distance between vertices u and v in G. In this paper, we study the Wiener indices of unicyclic graphs.Using a formulation for calculating the Wiener index of an unicyclic graph according its struction, we characterize the graphs the second largest Wiener indices among all the unicyclic graphs of order n.