Bethe graphs attached to the vertices of a connected graph: a spectral approach
Autor(a) principal: | |
---|---|
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/10773/16233 |
Resumo: | A weighted Bethe graph $B$ is obtained from a weighted generalized Bethe tree by identifying each set of children with the vertices of a graph belonging to a family $F$ of graphs. The operation of identifying the root vertex of each of $r$ weighted Bethe graphs to the vertices of a connected graph $\mathcal{R}$ of order $r$ is introduced as the $\mathcal{R}$-concatenation of a family of $r$ weighted Bethe graphs. It is shown that the Laplacian eigenvalues (when $F$ has arbitrary graphs) as well as the signless Laplacian and adjacency eigenvalues (when the graphs in $F$ are all regular) of the $\mathcal{R}$-concatenation of a family of weighted Bethe graphs can be computed (in a unified way) using the stable and low computational cost methods available for the determination of the eigenvalues of symmetric tridiagonal matrices. Unlike the previous results already obtained on this topic, the more general context of families of distinct weighted Bethe graphs is herein considered. |
id |
RCAP_d503de74f647534244ff842fa1c9b19d |
---|---|
oai_identifier_str |
oai:ria.ua.pt:10773/16233 |
network_acronym_str |
RCAP |
network_name_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository_id_str |
7160 |
spelling |
Bethe graphs attached to the vertices of a connected graph: a spectral approachGraph spectraGraph operationsLaplacian matrixSignless Laplacian matrixAdjacency matrixA weighted Bethe graph $B$ is obtained from a weighted generalized Bethe tree by identifying each set of children with the vertices of a graph belonging to a family $F$ of graphs. The operation of identifying the root vertex of each of $r$ weighted Bethe graphs to the vertices of a connected graph $\mathcal{R}$ of order $r$ is introduced as the $\mathcal{R}$-concatenation of a family of $r$ weighted Bethe graphs. It is shown that the Laplacian eigenvalues (when $F$ has arbitrary graphs) as well as the signless Laplacian and adjacency eigenvalues (when the graphs in $F$ are all regular) of the $\mathcal{R}$-concatenation of a family of weighted Bethe graphs can be computed (in a unified way) using the stable and low computational cost methods available for the determination of the eigenvalues of symmetric tridiagonal matrices. Unlike the previous results already obtained on this topic, the more general context of families of distinct weighted Bethe graphs is herein considered.Taylor & Francis2017-07-252017-07-25T00:00:00Z2018-07-25T14:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/16233eng0308-108710.1080/03081087.2016.1211081Andrade, EnideCardoso, Domingos M.Medina, LuisRojo, Oscarinfo: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:RCAAP2024-05-06T03:58:14Zoai:ria.ua.pt:10773/16233Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-06T03:58:14Repositório 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 |
Bethe graphs attached to the vertices of a connected graph: a spectral approach |
title |
Bethe graphs attached to the vertices of a connected graph: a spectral approach |
spellingShingle |
Bethe graphs attached to the vertices of a connected graph: a spectral approach Andrade, Enide Graph spectra Graph operations Laplacian matrix Signless Laplacian matrix Adjacency matrix |
title_short |
Bethe graphs attached to the vertices of a connected graph: a spectral approach |
title_full |
Bethe graphs attached to the vertices of a connected graph: a spectral approach |
title_fullStr |
Bethe graphs attached to the vertices of a connected graph: a spectral approach |
title_full_unstemmed |
Bethe graphs attached to the vertices of a connected graph: a spectral approach |
title_sort |
Bethe graphs attached to the vertices of a connected graph: a spectral approach |
author |
Andrade, Enide |
author_facet |
Andrade, Enide Cardoso, Domingos M. Medina, Luis Rojo, Oscar |
author_role |
author |
author2 |
Cardoso, Domingos M. Medina, Luis Rojo, Oscar |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Andrade, Enide Cardoso, Domingos M. Medina, Luis Rojo, Oscar |
dc.subject.por.fl_str_mv |
Graph spectra Graph operations Laplacian matrix Signless Laplacian matrix Adjacency matrix |
topic |
Graph spectra Graph operations Laplacian matrix Signless Laplacian matrix Adjacency matrix |
description |
A weighted Bethe graph $B$ is obtained from a weighted generalized Bethe tree by identifying each set of children with the vertices of a graph belonging to a family $F$ of graphs. The operation of identifying the root vertex of each of $r$ weighted Bethe graphs to the vertices of a connected graph $\mathcal{R}$ of order $r$ is introduced as the $\mathcal{R}$-concatenation of a family of $r$ weighted Bethe graphs. It is shown that the Laplacian eigenvalues (when $F$ has arbitrary graphs) as well as the signless Laplacian and adjacency eigenvalues (when the graphs in $F$ are all regular) of the $\mathcal{R}$-concatenation of a family of weighted Bethe graphs can be computed (in a unified way) using the stable and low computational cost methods available for the determination of the eigenvalues of symmetric tridiagonal matrices. Unlike the previous results already obtained on this topic, the more general context of families of distinct weighted Bethe graphs is herein considered. |
publishDate |
2017 |
dc.date.none.fl_str_mv |
2017-07-25 2017-07-25T00:00:00Z 2018-07-25T14:00:00Z |
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/10773/16233 |
url |
http://hdl.handle.net/10773/16233 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0308-1087 10.1080/03081087.2016.1211081 |
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 |
Taylor & Francis |
publisher.none.fl_str_mv |
Taylor & Francis |
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 |
mluisa.alvim@gmail.com |
_version_ |
1817543562326179840 |