Spectral radius and \(k\)-connectedness of a graph
type: Item
instance of: scholarly article
title: Spectral radius and \(k\)-connectedness of a graph
zbMATH Open document ID: 1391.05164
published in: Monatshefte für Mathematik
publication date: 2018-04-16T00:00:00Z
review text: Let \(\delta\geq k\geq 3\) and \(n\geq (\delta-k+2)(k^2-2k+4)+3\). The authors show that if a connected graph \(G\) with \(n\) vertices and minimum degree at least \(\delta\) satisfies \(\lambda_1(G)\geq n-\delta+k-3\), where \(\lambda_1(G)\) is the spectral radius of adjacency matrix of \(G\), then \(G\) is \(k\)-connected unless \(G\) is isomorphic to the join of \(K_{k-1}\) with \(K_{\delta-k+2}\cup K_{n-\delta-1}\). The same condition for \(\lambda_1(G)\) implies that \(G\) is always \(k\)-edge-connected.
reviewed by: Dragan Stevanović
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C12
Mathematics Subject Classification ID: 05C07
Mathematics Subject Classification ID: 05C35
zbMATH DE Number: 6860450
zbMATH Keywords: spectral radius
zbMATH Keywords: minimum degree
zbMATH Keywords: \(k\)-connectedness
zbMATH Keywords: \(k\)-edge-connectedness
author: Lihua Feng
author: Peng-Li Zhang
author: Weijun Liu
MaRDI profile type: Publication
full work available at URL: s00605-017-1055-9
OpenAlex ID: W2606028403
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DOI: 10.1007/S00605-017-1055-9
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description: scientific article; zbMATH DE number 6860450