Extraconnectivity of \(s\)-geodetic digraphs and graphs
type: Item
instance of: scholarly article
title: Extraconnectivity of \(s\)-geodetic digraphs and graphs
zbMATH Open document ID: 0927.05049
DOI: 10.1016/S0012-365X(98)00163-0
published in: Discrete Mathematics
publication date: 1999-12-05T00:00:00Z
review text: The \(\eta\)-extraconnectivity \(\kappa _\eta\) of a (di)graph \(G\) is the minimum cardinality of a set of vertices whose deletion disconnects \(G\) in such a way that all remaining (strongly) connected components have cardinality greater than \(\eta\). A (di)graph \(G\) with diameter \(D>1\) is said to be \(s\)-geodetic, \(1\leq s\leq D\), if for any two of its vertices \(x\) and \(y\) there exists at most one \(x\)-\(y\) path of length not exceeding \(s\). Starting from results of the paper by \textit{C. Balbuena, A. Carmona, J. Fábrega} and \textit{M. A. Fiol} [Discrete Math. 167/168, 85-100 (1997; Zbl 0874.05033)] sufficient conditions are given to assure the maximum \(\eta\)-extraconnectivity of such a digraph with minimum degree \(\delta\). Similar conditions are given for \(s\)-geodetic digraphs. The corresponding edge versions of these results are also discussed.
reviewed by: Ján Plesník
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C20
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C38
zbMATH DE Number: 1320575
zbMATH Keywords: connectivity
zbMATH Keywords: extraconnectivity
zbMATH Keywords: degree
zbMATH Keywords: diameter
zbMATH Keywords: \(s\)-geodetic digraph
author: C. Balbuena
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1320575