Locating Eigenvalues of Perturbed Laplacian Matrices of Trees

Detalhes bibliográficos
Autor(a) principal: BRAGA,R.O.
Data de Publicação: 2017
Outros Autores: RODRIGUES,V.M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300479
Resumo: ABSTRACT We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees. Using our method we characterize the trees that have up to 5 distinct eigenvalues with respect to a family of perturbed Laplacian matrices that includes the adjacency and normalized Laplacian matrices as special cases, among others.
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spelling Locating Eigenvalues of Perturbed Laplacian Matrices of Treesperturbed Laplacian matrixeigenvalue locationtreesABSTRACT We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees. Using our method we characterize the trees that have up to 5 distinct eigenvalues with respect to a family of perturbed Laplacian matrices that includes the adjacency and normalized Laplacian matrices as special cases, among others.Sociedade Brasileira de Matemática Aplicada e Computacional2017-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300479TEMA (São Carlos) v.18 n.3 2017reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2017.018.03.0479info:eu-repo/semantics/openAccessBRAGA,R.O.RODRIGUES,V.M.eng2018-02-08T00:00:00Zoai:scielo:S2179-84512017000300479Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2018-02-08T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
spellingShingle Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
BRAGA,R.O.
perturbed Laplacian matrix
eigenvalue location
trees
title_short Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title_full Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title_fullStr Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title_full_unstemmed Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
title_sort Locating Eigenvalues of Perturbed Laplacian Matrices of Trees
author BRAGA,R.O.
author_facet BRAGA,R.O.
RODRIGUES,V.M.
author_role author
author2 RODRIGUES,V.M.
author2_role author
dc.contributor.author.fl_str_mv BRAGA,R.O.
RODRIGUES,V.M.
dc.subject.por.fl_str_mv perturbed Laplacian matrix
eigenvalue location
trees
topic perturbed Laplacian matrix
eigenvalue location
trees
description ABSTRACT We give a linear time algorithm to compute the number of eigenvalues of any perturbed Laplacian matrix of a tree in a given real interval. The algorithm can be applied to weighted or unweighted trees. Using our method we characterize the trees that have up to 5 distinct eigenvalues with respect to a family of perturbed Laplacian matrices that includes the adjacency and normalized Laplacian matrices as special cases, among others.
publishDate 2017
dc.date.none.fl_str_mv 2017-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300479
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512017000300479
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2017.018.03.0479
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.18 n.3 2017
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
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reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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