Upper bounds on the Laplacian energy of some graphs

Detalhes bibliográficos
Autor(a) principal: Robbiano, M.
Data de Publicação: 2010
Outros Autores: Martins, E. A., Jiménez, R., Martín, B. S.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10773/4287
Resumo: The Laplacian energy L£[G] of a simple graph G with n vertices and m edges is equal to the sum of distances of the Laplacian eigenvalues to their average. For 1 ≤ j ≤ s, let Aj be matrices of orders n j. Suppose that det(L(G) - λIn) = Πj=1s det(Aj- - λI n,j)tj, with tj > 0. In the present paper we prove LE[G) ≤ Σ j=1stj√n j||Aj-2m/n||F≤ √n||L(G) - 2m/nIn||F , where ||·||F stands for the Frobenius matrix norm.
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spelling Upper bounds on the Laplacian energy of some graphsLaplacian matrixGraphBethe treeLaplacian energyThe Laplacian energy L£[G] of a simple graph G with n vertices and m edges is equal to the sum of distances of the Laplacian eigenvalues to their average. For 1 ≤ j ≤ s, let Aj be matrices of orders n j. Suppose that det(L(G) - λIn) = Πj=1s det(Aj- - λI n,j)tj, with tj > 0. In the present paper we prove LE[G) ≤ Σ j=1stj√n j||Aj-2m/n||F≤ √n||L(G) - 2m/nIn||F , where ||·||F stands for the Frobenius matrix norm.University of Kragujevac10000-01-01T00:00:00Z2010-01-01T00:00:00Z2010info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/4287eng0340-6253Robbiano, M.Martins, E. A.Jiménez, R.Martín, B. S.info: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:RCAAP2024-02-22T11:04:35Zoai:ria.ua.pt:10773/4287Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T02:42:14.592793Repositório 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 Upper bounds on the Laplacian energy of some graphs
title Upper bounds on the Laplacian energy of some graphs
spellingShingle Upper bounds on the Laplacian energy of some graphs
Robbiano, M.
Laplacian matrix
Graph
Bethe tree
Laplacian energy
title_short Upper bounds on the Laplacian energy of some graphs
title_full Upper bounds on the Laplacian energy of some graphs
title_fullStr Upper bounds on the Laplacian energy of some graphs
title_full_unstemmed Upper bounds on the Laplacian energy of some graphs
title_sort Upper bounds on the Laplacian energy of some graphs
author Robbiano, M.
author_facet Robbiano, M.
Martins, E. A.
Jiménez, R.
Martín, B. S.
author_role author
author2 Martins, E. A.
Jiménez, R.
Martín, B. S.
author2_role author
author
author
dc.contributor.author.fl_str_mv Robbiano, M.
Martins, E. A.
Jiménez, R.
Martín, B. S.
dc.subject.por.fl_str_mv Laplacian matrix
Graph
Bethe tree
Laplacian energy
topic Laplacian matrix
Graph
Bethe tree
Laplacian energy
description The Laplacian energy L£[G] of a simple graph G with n vertices and m edges is equal to the sum of distances of the Laplacian eigenvalues to their average. For 1 ≤ j ≤ s, let Aj be matrices of orders n j. Suppose that det(L(G) - λIn) = Πj=1s det(Aj- - λI n,j)tj, with tj > 0. In the present paper we prove LE[G) ≤ Σ j=1stj√n j||Aj-2m/n||F≤ √n||L(G) - 2m/nIn||F , where ||·||F stands for the Frobenius matrix norm.
publishDate 2010
dc.date.none.fl_str_mv 10000-01-01T00:00:00Z
2010-01-01T00:00:00Z
2010
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/10773/4287
url http://hdl.handle.net/10773/4287
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0340-6253
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 University of Kragujevac
publisher.none.fl_str_mv University of Kragujevac
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
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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
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