Abstract
The hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener indexWW(G) is defined as WW(G) = (1/2) Sigma(u,v epsilon 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.. vertices and diameter.. and characterize the corresponding extremal graphs.