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A lower bound for the energy of symmetric matrices and graphs

Bibliographic Details
Main Author: Andrade, Enide
Publication Date: 2017
Other Authors: Robbiano, María, Martín, B. San
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10773/16240
Summary: 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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spelling 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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T03:58:15Zoai:ria.ua.pt:10773/16240Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:52:45.317261Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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