Boundary vertices in graphs
type: Item
instance of: scholarly article
title: Boundary vertices in graphs
zbMATH Open document ID: 1020.05024
DOI: 10.1016/S0012-365X(02)00567-8
author: Gary Chartrand
author: D. Erwin
author: Garry Johns
author: Ping Zhang
published in: Discrete Mathematics
publication date: 2003-04-09T00:00:00Z
review text: A vertex \(u\) is a boundary vertex of a nontrivial connected graph \(G\) if there is a vertex \(v\) of \(G\) such that (the distance) \(d(w,v)\leq d(u,v)\) for all neighbors \(w\) of \(u\). The subgraph of \(G\) induced by its boundary vertices is the boundary \(\partial (G)\) of \(G\). The authors study the relationship among the periphery Per\((G)\) [\textit{H. Bielak} and \textit{M. M. Syslo}, Stud. Sci. Math. Hung. 18, 269-275 (1983; Zbl 0569.05030)], eccentric subgraph \(\text{Ecc}(G)\) [\textit{G. Chartrand, W. Gu, M. Schultz} and \textit{S. J. Winters}, Networks 34, 115-121 (1999; Zbl 0959.90062)], and boundary \(\partial (G)\) of a connected graph \(G\). Also a characterization of all boundary graphs is established.
reviewed by: Ján Plesník
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 1896000
zbMATH Keywords: graph
zbMATH Keywords: distance
zbMATH Keywords: peripheral vertex
zbMATH Keywords: eccentric vertex
zbMATH Keywords: boundary vertex
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00567-8
OpenAlex ID: W2070408685
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description: scientific article; zbMATH DE number 1896000