The Hyper-Wiener Index of Trees of Order n with Diameter d

الملخص EN

The hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds.

The hyper-Wiener index W W ( G ) is defined as W W ( G ) = 1 / 2 ∑ u , v ∈ V G d G u , v + d G 2 u , v with the summation going over all pairs of vertices in G , and d G u , v denotes the distance of the two vertices u and v in the graph G .

In this paper, we obtain the second-minimum hyper-Wiener indices among all the trees with n vertices and diameter d and characterize the corresponding extremal graphs.