A Wiener-type graph invariant for some bipartite graphs
type: Item
instance of: scholarly article
title: A Wiener-type graph invariant for some bipartite graphs
zbMATH Open document ID: 0839.05037
DOI: 10.1016/0893-9659(95)00067-Z
author: Andrey A. Dobrynin
author: Ivan Gutman
author: Gyula Dömötör
published in: Applied Mathematics Letters
publication date: 1995-12-20T00:00:00Z
review text: The Wiener number (index) of a connected graph \(G\) is the sum \(W(G)\) of distances between all pairs of vertices of \(G\). In this paper, a similar invariant is considered: the sum \(W^*(G)\) of the products \(n_u(e)n_v(e)\) over all edges \(e= (u, v)\), where \(n_u(e)\) is the number of vertices of \(G\) lying closer to \(u\) than to \(v\). A class of bipartite graphs is shown to have the same property for \(W\) and \(W^*\).
reviewed by: Ján Plesník
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 828425
zbMATH Keywords: Wiener number
zbMATH Keywords: distances
zbMATH Keywords: bipartite graphs
MaRDI profile type: Publication
cites work: Q4692391
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cites work: Distance in graphs
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full work available at URL: 0893-9659(95)00067-z
OpenAlex ID: W2067310719
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description: scientific article; zbMATH DE number 828425