给定直径的单圈图的Harary指数

On the Harary Index of Unicycle Graphs with Given Diameter

连通图G的Harary指数是指图G中所有点对的距离的倒数之和。主要研究固定直径的单圈图的极大Harary指数及相对应的极图。特别地,当4≤d≤n-3,且d≡0(mod2)时,得到第二大Harary指数的极图。

The Harary index is defined as the sum of reciprocals of distance over all pairs of vertices of a connected graph. This paper gives the largest Harary index of unicycle graphs with given diameter and characterizes the extreme graphs attaining the upper bound. Specially,we also obtained the second largest extreme graphs when 4 ≤ d ≤ n-3 and d ≡ 0( mod2).