Upper bounds on the Laplacian energy of some graphs
| Autor(a) principal: | |
|---|---|
| Data de Publicação: | 2010 |
| Outros Autores: | , , |
| Tipo de documento: | Artigo |
| Idioma: | eng |
| Título da fonte: | Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) |
| 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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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:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-05-06T03:33:25Zoai:ria.ua.pt:10773/4287Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T13:38:41.094799Repositórios 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 |
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 |
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eng |
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eng |
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0340-6253 |
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info:eu-repo/semantics/openAccess |
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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 |
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reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia instacron:RCAAP |
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FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia |
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RCAAP |
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RCAAP |
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Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) |
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Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) |
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Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia |
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info@rcaap.pt |
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