The hyper-Wiener index of trees of order \(n\) with diameter \(d\)
Summary: 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 \(W W(G) = \left(1 / 2\right) \sum_{u, v \in V \left(G\right)} \left(d_G \left(u, v\right) + d_G^2 \left(u, v\right)\right)\) with the summation going over all pairs of vertices in \(G\), and \(d_G \left(u, v\right)\) 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.
scientific article; zbMATH DE number 6806286