The connected cutset connectivity of a graph
type: Item
instance of: scholarly article
title: The connected cutset connectivity of a graph
zbMATH Open document ID: 0643.05044
DOI: 10.1016/0012-365X(88)90058-1
author: Ortrud R. Oellermann
published in: Discrete Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The connected (edge-)cutset connectivity \(c\kappa\) (G) \((c\kappa_ 1(G))\) of a graph G is the minimum cardinality of a vertex (edge) cutset S of G such that the subgraph induced by S is connected. Let \(\kappa\) (G) be the vertex-connectivity of G, \(\kappa_ 1(G)\) the edge-connectivity and \(\delta\) (G) the minimal degree. The author proves existence theorems for graphs with given \(\kappa\) (G), \(c\kappa\) (G), \(\delta\) (G) as well as given \(\kappa_ 1(G)\), \(c\kappa_ 1(G)\), \(\delta\) (G) and shows that for graphs with \(c\kappa_ 1(G)\subseteq c\kappa (G)\) holds \(c\kappa_ 1(G)=\delta (G)\).
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 4047766
zbMATH Keywords: minimum degree
zbMATH Keywords: edge-connectivity
reviewed by: Michael Hager
MaRDI profile type: Publication
cites work: A Graph-Theoretic Approach to a Communications Problem
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description: scientific article; zbMATH DE number 4047766