On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree
type: Item
instance of: scholarly article
title: On the multiplicities of eigenvalues of a Hermitian matrix whose graph is a tree
zbMATH Open document ID: 1144.15003
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 2008-06-24T00:00:00Z
review text: The author gives alternative and simpler proofs of some results of \textit{C. R. Johnson} and \textit{A. L. Duarte} [Linear Multilinear Algebra 46, No. 1--2, 139--144 (1999; Zbl 0929.15005)] and \textit{C. R. Johnson} and \textit{C. M. Saiago} [Electron J. Linear Algebra 9, 27--31 (2002; Zbl 0999.15005)] on the minimum number of vertex disjoint paths, occuring as induced subgraphs of a tree \(T\), which cover all the vertices of \(T\). The approach is based on classic results of \textit{O. J. Heilmann} and \textit{E. H. Lieb} [Commun. Math. Phys. 25, 190--232 (1972; Zbl 0228.05131)] from the theory of matching polynomials.
reviewed by: Dragan Stevanović
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 5292345
zbMATH Keywords: eigenvalues
zbMATH Keywords: graph
zbMATH Keywords: tree
zbMATH Keywords: symmetric matrices
zbMATH Keywords: vertex degrees
author: C. M.da Fonseca
MaRDI profile type: Publication
full work available at URL: s10231-007-0044-3
OpenAlex ID: W2153360654
cites work: Q4052166
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DOI: 10.1007/S10231-007-0044-3
description: scientific article; zbMATH DE number 5292345