关于给定直径的单圈图的Wiener指标

On the Wiener Index of Unicyclic Graphs with Fixed Diameter

摘要: 一个图的Wiener指标被定义为W(G)=∑u,vV(G)dG(u,v)，其中dG(u,v)是G中u, v间的距离。本文得到了在所有直径为d的n阶单圈图中，具有最小Wiener指标的极图。特别地，当4≤d≤n－3，且d≡0(mod 2)时，具有次小Wiener指标的极图也被得到。

Abstract: The Wiener index is defined as W(G)=∑u,vV(G)dG(u,v), where dG(u,v) is the distance between u and v in G. In this paper, we obtain the graph with the least Wiener index among all the unicyclic graphs with n vertices and diameter d. Moreover, if 4≤d≤n－3, d≡0(mod 2), then the unicyclic graphs with the second least Wiener index are obtained.