The median procedure on median graphs
type: Item
instance of: scholarly article
title: The median procedure on median graphs
zbMATH Open document ID: 0906.05023
DOI: 10.1016/S0166-218X(98)00003-1
author: Henry Martyn Mulder
author: Fred Roberts
author: F. R. McMorris
published in: Discrete Applied Mathematics
publication date: 1999-02-14T00:00:00Z
full work available at URL: dam
review text: An ordered \(k\)-tuple \(\pi= (x_1,\dots, x_k)\) of elements of a finite metric space \((X, d)\) is called a profile. An element \(x\in X\) for which \(\sum^k_{i= 1}d(x, x_i)\) is minimum is called a median of \(\pi\). The median procedure is the function \(\text{Med}(\pi)= \{x\mid x\) is a median of \(\pi\}\). These concepts are studied in the case when \(X\) is the vertex set of a graph with the usual distance. In particular, they are studied for median graphs, i.e. connected graphs \(G\) in which for any three vertices \(x\), \(y\), \(z\) there is a unique vertex \(w\) on the geodesic between each pair of \(x\), \(y\), \(z\). Special attention is paid to cube-free median graphs.
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 1180361
zbMATH Keywords: profile
zbMATH Keywords: median
zbMATH Keywords: distance
reviewed by: Bohdan Zelinka
MaRDI profile type: Publication
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OpenAlex ID: W2004433054
description: scientific article; zbMATH DE number 1180361