On minimal embedding of two graphs as center and periphery
type: Item
instance of: scholarly article
title: On minimal embedding of two graphs as center and periphery
zbMATH Open document ID: 0790.05044
DOI: 10.1007/BF02988319
author: Weizhen Gu
published in: Graphs and Combinatorics
publication date: 1994-06-22T00:00:00Z
review text: As usual, the distance \(d(u,v)\) between two vertices of a graph is the length of the shortest path joining them. The eccentricity of a vertex \(u\), denoted \(e(u)\), is the maximum of the quantities \(d(u,v)\), where \(v\) ranges over the vertex set. The minimum of the vertex eccentricities of a graph is known as the radius of \(G\) and is denoted \(r(G)\). The maximum of the vertex eccentricities is the diameter of \(G\) and is denoted \(\text{dia}(G)\). The center of \(G\) is the subgraph induced by the set of vertices \(v\) with \(e(v)=\text{dia}(G)\). For graphs \(G_ 1\) and \(G_ 2\) and an integer \(d\), \(2\leq d\leq r(G_ 2)\), let \(\Gamma\) be the set of all graphs \(G\) so that \(G_ 1\) is the center of \(G\) and \(G_ 2\) is the periphery. Let \(\Gamma_ d\) be the subset of \(\Gamma\) where \(\text{dia}(G)=d\). Define \(\beta(G_ 1,G_ 2)\) to be the minimum of the number of vertices of \(G\), \(G\in\Gamma\). Define \(\beta(G_ 1,G_ 2,d)\) to be the minimum of the number of vertices of \(G\), \(G\in\Gamma_ d\). The paper under review investigates the values of \(\beta(G_ 1,G_ 2)\) and the upper bound of \(\beta(G_ 1,G_ 2,d)\).
reviewed by: M.Marx
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 490738
zbMATH Keywords: distance
zbMATH Keywords: eccentricity
zbMATH Keywords: radius
zbMATH Keywords: diameter
zbMATH Keywords: center
zbMATH Keywords: upper bound
MaRDI profile type: Publication
cites work: Q3686741
cites work: Q4739946
cites work: Diameters in graphs
cites work: Q3987057
full work available at URL: https://doi.org/10.1007/bf02988319
OpenAlex ID: W2013655552
description: scientific article; zbMATH DE number 490738