关于给定直径的单圈图的Wiener指标
On the Wiener Index of Unicyclic Graphs with Fixed Diameter
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摘要: 一个图的Wiener指标被定义为W(G)=∑u,vV(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,vV(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.