Extremal values for ratios of distances in trees
type: Item
instance of: scholarly article
title: Extremal values for ratios of distances in trees
zbMATH Open document ID: 0886.05059
DOI: 10.1016/S0166-218X(97)00068-1
published in: Discrete Applied Mathematics
publication date: 1998-04-08T00:00:00Z
full work available at URL: dam
review text: The authors study the distance parameters of a connected graph \(G\): \[ \sigma(u):=\sum_{v\in V(G)}d(u,v) \quad\text{and}\quad \sigma(G):=\frac 12\sum_{u\in V(G)}\sigma(u), \] in the case of trees. Extremal values for the ratios \(\sigma(T)/ \sigma(v)\), \(\sigma(T)/\sigma(w)\), \(\sigma(w)/\sigma(v)\), and \(\sigma(w)/\sigma(u)\) are determined, where \(T\) is a tree of order \(n\), \(v\) is a centroid vertex of \(T\), and \(w\) and \(u\) are end vertices of \(T\).
reviewed by: Ján Plesník
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C05
zbMATH DE Number: 1109899
zbMATH Keywords: distance
zbMATH Keywords: Wiener index
zbMATH Keywords: transmission
zbMATH Keywords: status
zbMATH Keywords: tree
author: Curtiss Barefoot
author: R. C. Entringer
author: László A. Székely
MaRDI profile type: Publication
cites work: Q4871152
cites work: Q4351067
cites work: Distance in graphs
cites work: Q4882555
cites work: Q4325295
cites work: The complexity of the network design problem
cites work: On the sum of all distances in a graph or digraph
cites work: Q4280250
cites work: Mean distance in a tree
cites work: Q5606538
OpenAlex ID: W2077737311
description: scientific article; zbMATH DE number 1109899