Wiener number of vertex-weighted graphs and a chemical application
type: Item
instance of: scholarly article
title: Wiener number of vertex-weighted graphs and a chemical application
zbMATH Open document ID: 0889.05046
DOI: 10.1016/S0166-218X(97)00070-X
author: Ivan Gutman
author: Sandi Klavžar
published in: Discrete Applied Mathematics
publication date: 1998-06-11T00:00:00Z
full work available at URL: dam
review text: The Wiener number of a weighted, connected graph \((G,w)\) is defined as \[ W(G,w)= \sum_{\{u,v\} \subseteq V(G)} w(u)w(v) d_G(u,v) \] where \(d_G(u,v)\) is the distance between \(u\) and \(v\) in \(G\). A graph \(G\) is called a partial binary Hamming graph if each vertex \(v\) can be labelled by a word of fixed length, \(\ell(v)\), defined on the alphabet \(\{0,1\}\) such that for all \(u,v\in V(G)\) the distance between \(u\) and \(v\) is the Hamming distance between \(\ell(u)\) and \(\ell(v)\). A formula is developed for computing \(W(G,w)\) for such graphs \(G\). This formula is then used to express the Wiener number of the chemical graphs associated with phenylenes in terms of certain simpler related graphs.
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C90
Mathematics Subject Classification ID: 92E10
zbMATH DE Number: 1109901
zbMATH Keywords: Wiener number
zbMATH Keywords: Hamming graph
zbMATH Keywords: Hamming distance
reviewed by: R. C. Entringer
MaRDI profile type: Publication
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OpenAlex ID: W2104803612
description: scientific article; zbMATH DE number 1109901