\(\ell\)-connectivity, integrity, tenacity, toughness and eigenvalues of graphs
type: Item
instance of: scholarly article
title: \(\ell\)-connectivity, integrity, tenacity, toughness and eigenvalues of graphs
zbMATH Open document ID: 1501.05015
author: Hongzhang Chen
author: Jianxi Li
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2022-10-31T00:00:00Z
review text: The \(\ell\)-edge connectivity \(\kappa_\ell(G)\) of a simple graph \(G\) is the minimum number of vertices of \(G\) whose removal produces either a disconnected graph with at least \(\ell\) components or a graph with fewer than \(\ell\) vertices. The first two main results of the paper under review provide sufficient conditions for the bound \(\kappa_\ell(G)\geq k\) to hold, where \(\ell\geq k\geq 2\), expressed in terms of bounds involving other invariants on \(G\) including the maximum degree \(\Delta\), the minimum degree \(\delta\), the edge connectivity \(\kappa'\), the girth \(g(G)\), the clique number \(\omega(G)\), and eigenvalues \(\lambda_i\) of \(G\). Lower bounds on the integrity \(I(G)\), tenacity \(T(G)\) and toughness \(t(G)\) are also provided, expressed in terms of \(\Delta\), \(\kappa'\), the number of vertices \(n\), the Laplacian eigenvalue \(\mu_{n-1}\) and the normalised Laplacian eigenvalues \(\rho_i\). Some of these results extend previous results in the literature.
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 7610173
zbMATH Keywords: eigenvalues
zbMATH Keywords: \(\ell\)-connectivity
zbMATH Keywords: integrity
zbMATH Keywords: tenacity
zbMATH Keywords: toughness
reviewed by: Thomas Britz
MaRDI profile type: Publication
full work available at URL: s40840-022-01381-2
OpenAlex ID: W4294176233
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DOI: 10.1007/S40840-022-01381-2
description: scientific article; zbMATH DE number 7610173