A lower bound for the energy of symmetric matrices and graphs
Autor(a) principal: | |
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Data de Publicação: | 2017 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10773/16240 |
Resumo: | The energy of a symmetric matrix is the sum of the absolute values of its eigenvalues. We introduce a lower bound for the energy of a symmetric partitioned matrix into blocks. This bound is related to the spectrum of its quotient matrix. Furthermore, we study necessary conditions for the equality. Applications to the energy of the generalized composition of a family of arbitrary graphs are obtained. A lower bound for the energy of a graph with a bridge is given. Some computational experiments are presented in order to show that, in some cases, the obtained lower bound is incomparable with the well known lower bound $2\sqrt{m}$, where $m$ is the number of edges of the graph. |
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7160 |
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A lower bound for the energy of symmetric matrices and graphsSpectral graph theoryEnergy of graphsThe energy of a symmetric matrix is the sum of the absolute values of its eigenvalues. We introduce a lower bound for the energy of a symmetric partitioned matrix into blocks. This bound is related to the spectrum of its quotient matrix. Furthermore, we study necessary conditions for the equality. Applications to the energy of the generalized composition of a family of arbitrary graphs are obtained. A lower bound for the energy of a graph with a bridge is given. Some computational experiments are presented in order to show that, in some cases, the obtained lower bound is incomparable with the well known lower bound $2\sqrt{m}$, where $m$ is the number of edges of the graph.Elsevier2018-07-20T14:00:56Z2017-01-15T00:00:00Z2017-01-152018-01-15T15:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16240eng0024-379510.1016/j.laa.2016.10.022Andrade, EnideRobbiano, MaríaMartín, B. Saninfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-02-22T11:30:13Zoai:ria.ua.pt:10773/16240Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:51:24.049278Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A lower bound for the energy of symmetric matrices and graphs |
title |
A lower bound for the energy of symmetric matrices and graphs |
spellingShingle |
A lower bound for the energy of symmetric matrices and graphs Andrade, Enide Spectral graph theory Energy of graphs |
title_short |
A lower bound for the energy of symmetric matrices and graphs |
title_full |
A lower bound for the energy of symmetric matrices and graphs |
title_fullStr |
A lower bound for the energy of symmetric matrices and graphs |
title_full_unstemmed |
A lower bound for the energy of symmetric matrices and graphs |
title_sort |
A lower bound for the energy of symmetric matrices and graphs |
author |
Andrade, Enide |
author_facet |
Andrade, Enide Robbiano, María Martín, B. San |
author_role |
author |
author2 |
Robbiano, María Martín, B. San |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Andrade, Enide Robbiano, María Martín, B. San |
dc.subject.por.fl_str_mv |
Spectral graph theory Energy of graphs |
topic |
Spectral graph theory Energy of graphs |
description |
The energy of a symmetric matrix is the sum of the absolute values of its eigenvalues. We introduce a lower bound for the energy of a symmetric partitioned matrix into blocks. This bound is related to the spectrum of its quotient matrix. Furthermore, we study necessary conditions for the equality. Applications to the energy of the generalized composition of a family of arbitrary graphs are obtained. A lower bound for the energy of a graph with a bridge is given. Some computational experiments are presented in order to show that, in some cases, the obtained lower bound is incomparable with the well known lower bound $2\sqrt{m}$, where $m$ is the number of edges of the graph. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-01-15T00:00:00Z 2017-01-15 2018-07-20T14:00:56Z 2018-01-15T15:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10773/16240 |
url |
http://hdl.handle.net/10773/16240 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0024-3795 10.1016/j.laa.2016.10.022 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Elsevier |
publisher.none.fl_str_mv |
Elsevier |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799137563699576832 |