关于给定直径的单圈图的Wiener指标

On the Wiener Index of Unicyclic Graphs with Fixed Diameter

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。

The Wiener index is defined as W（G）=∑dG（u,v）where dc;（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（mod 2）, then theunicyclic graphs with the second least Wiener index are obtained.