The hyper-Wiener index of trees of order \(n\) with diameter \(d\)
type: Item
instance of: scholarly article
title: The hyper-Wiener index of trees of order \(n\) with diameter \(d\)
zbMATH Open document ID: 1373.05047
DOI: 10.1155/2016/7241349
author: Gaixiang Cai
author: Ahmed Alsaedi
author: Guidong Yu
author: Jinde Cao
author: Fuad E. Alsaadi
published in: Discrete Dynamics in Nature and Society
publication date: 2017-11-13T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 6806286
zbMATH Keywords: second-minimum hyper-Wiener index
Wikidata QID: Q59123629
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/7241349
OpenAlex ID: W2521169697
cites work: Zagreb, Harary and hyper-Wiener indices of graphs with a given matching number
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description: scientific article; zbMATH DE number 6806286