给定悬挂点数图的Harary指数的极图

Extremal Graph for the Harary Index of Graphs on the Given Number of Suspension Point

图的Harary指数定义为图中所有顶点对的距离的倒数之和。本文我们刻画了给定顶点数和悬挂点数的图类中,Harary指数取到最大、第二大、第三大的极图,并由此确定了关于悬挂点数的Harary指数上界。

The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paper, we characterize the extremal graph with the maximum, the second and the third largest Harary index among all graphs with given order and suspension point, and give an upper bound for the Harary index with the number of suspension pmnt.