On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle
type: Item
instance of: scholarly article
title: On the maximum multiplicity of an eigenvalue in a matrix whose graph contains exactly one cycle
zbMATH Open document ID: 1121.15013
author: Rosário Fernandes
published in: Linear Algebra and its Applications
publication date: 2007-03-09T00:00:00Z
review text: \textit{C. R. Johnson} and \textit{A. L. Duarte} [Linear Multilinear Algebra 46, No. 1--2, 139--144 (1999; Zbl 0929.15005)] proved that for trees \(G\) the maximum possible multiplicity \(M(G)\) of an eigenvalue of a Hermitian matrix whose graph is \(G\) equals the path-covering number of \(G\). The present paper establishes analogous results for some cases of matrices \(G\) whose graph contains exactly one cycle, relating \(M(G)\) to certain parameters associated with \(G\).
reviewed by: Erwin O. Kreyszig
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15B57
zbMATH DE Number: 5132609
zbMATH Keywords: eigenvalues
zbMATH Keywords: Hermitian matrices
MaRDI profile type: Publication
full work available at URL: j.laa.2006.06.030
OpenAlex ID: W2008062439
cites work: Computation of minimal rank and path cover number for certain graphs
cites work: The Construction of Jacobi and Periodic Jacobi Matrices With Prescribed Spectra
cites work: Problems in algebraic combinatorics
cites work: Matrix Analysis
cites work: The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree
cites work: On the Eigenvalues and Eigenvectors of a Class of Matrices
cites work: Spectral multiplicity and splitting results for a class of qualitative matrices
DOI: 10.1016/J.LAA.2006.06.030
description: scientific article; zbMATH DE number 5132609