Distance matrices on the H-join of graphs: A general result and applications
Autor(a) principal: | |
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Data de Publicação: | 2018 |
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/10773/24082 |
Resumo: | Given a graph $H$ with vertices $1,\ldots ,s$ and a set of pairwise vertex disjoint graphs $G_{1},\ldots ,G_{s},$ the vertex $i$ of $H$ is assigned to $G_{i}.$ Let $G$ be the graph obtained from the graphs $G_{1},\ldots ,G_{s}$ and the edges connecting each vertex of $G_{i}$ with all the vertices of $G_{j}$ for all edge $ij$ of $H.$ The graph $G$ is called the $H-join$ of $G_1,\ldots,G_s$. Let $M(G)$ be a matrix on a graph $G$. A general result on the eigenvalues of $M\left( G\right) $, when the all ones vector is an eigenvector of $M\left( G_{i}\right) $ for $i=1,2,\ldots ,s$, is given. This result is applied to obtain the distance eigenvalues, the distance Laplacian eigenvalues and as well as the distance signless Laplacian eigenvalues of $G$ when $G_{1},\ldots ,G_{s}$ are regular graphs. Finally, we introduce the notions of the distance incidence energy and distance Laplacian-energy like of a graph and we derive sharp lower bounds on these two distance energies among all the connected graphs of prescribed order in terms of the vertex connectivity. The graphs for which those bounds are attained are characterized. |
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Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
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7160 |
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Distance matrices on the H-join of graphs: A general result and applicationsGraph operationsVetex connectivityDistance matrixEigenvaluesDistance incidence energyDistance Laplacian-energy likeGiven a graph $H$ with vertices $1,\ldots ,s$ and a set of pairwise vertex disjoint graphs $G_{1},\ldots ,G_{s},$ the vertex $i$ of $H$ is assigned to $G_{i}.$ Let $G$ be the graph obtained from the graphs $G_{1},\ldots ,G_{s}$ and the edges connecting each vertex of $G_{i}$ with all the vertices of $G_{j}$ for all edge $ij$ of $H.$ The graph $G$ is called the $H-join$ of $G_1,\ldots,G_s$. Let $M(G)$ be a matrix on a graph $G$. A general result on the eigenvalues of $M\left( G\right) $, when the all ones vector is an eigenvector of $M\left( G_{i}\right) $ for $i=1,2,\ldots ,s$, is given. This result is applied to obtain the distance eigenvalues, the distance Laplacian eigenvalues and as well as the distance signless Laplacian eigenvalues of $G$ when $G_{1},\ldots ,G_{s}$ are regular graphs. Finally, we introduce the notions of the distance incidence energy and distance Laplacian-energy like of a graph and we derive sharp lower bounds on these two distance energies among all the connected graphs of prescribed order in terms of the vertex connectivity. The graphs for which those bounds are attained are characterized.Elsevier2020-12-01T00:00:00Z2018-09-07T00:00:00Z2018-09-07info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10773/24082eng0024-379510.1016/j.laa.2018.08.024Cardoso, Domingos M.Díaz, Roberto C.Rojo, Oscarinfo:eu-repo/semantics/embargoedAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2024-05-06T04:17:00Zoai:ria.ua.pt:10773/24082Portal AgregadorONGhttps://www.rcaap.pt/oai/openairemluisa.alvim@gmail.comopendoar:71602024-05-06T04:17Repositório 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 |
Distance matrices on the H-join of graphs: A general result and applications |
title |
Distance matrices on the H-join of graphs: A general result and applications |
spellingShingle |
Distance matrices on the H-join of graphs: A general result and applications Cardoso, Domingos M. Graph operations Vetex connectivity Distance matrix Eigenvalues Distance incidence energy Distance Laplacian-energy like |
title_short |
Distance matrices on the H-join of graphs: A general result and applications |
title_full |
Distance matrices on the H-join of graphs: A general result and applications |
title_fullStr |
Distance matrices on the H-join of graphs: A general result and applications |
title_full_unstemmed |
Distance matrices on the H-join of graphs: A general result and applications |
title_sort |
Distance matrices on the H-join of graphs: A general result and applications |
author |
Cardoso, Domingos M. |
author_facet |
Cardoso, Domingos M. Díaz, Roberto C. Rojo, Oscar |
author_role |
author |
author2 |
Díaz, Roberto C. Rojo, Oscar |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
Cardoso, Domingos M. Díaz, Roberto C. Rojo, Oscar |
dc.subject.por.fl_str_mv |
Graph operations Vetex connectivity Distance matrix Eigenvalues Distance incidence energy Distance Laplacian-energy like |
topic |
Graph operations Vetex connectivity Distance matrix Eigenvalues Distance incidence energy Distance Laplacian-energy like |
description |
Given a graph $H$ with vertices $1,\ldots ,s$ and a set of pairwise vertex disjoint graphs $G_{1},\ldots ,G_{s},$ the vertex $i$ of $H$ is assigned to $G_{i}.$ Let $G$ be the graph obtained from the graphs $G_{1},\ldots ,G_{s}$ and the edges connecting each vertex of $G_{i}$ with all the vertices of $G_{j}$ for all edge $ij$ of $H.$ The graph $G$ is called the $H-join$ of $G_1,\ldots,G_s$. Let $M(G)$ be a matrix on a graph $G$. A general result on the eigenvalues of $M\left( G\right) $, when the all ones vector is an eigenvector of $M\left( G_{i}\right) $ for $i=1,2,\ldots ,s$, is given. This result is applied to obtain the distance eigenvalues, the distance Laplacian eigenvalues and as well as the distance signless Laplacian eigenvalues of $G$ when $G_{1},\ldots ,G_{s}$ are regular graphs. Finally, we introduce the notions of the distance incidence energy and distance Laplacian-energy like of a graph and we derive sharp lower bounds on these two distance energies among all the connected graphs of prescribed order in terms of the vertex connectivity. The graphs for which those bounds are attained are characterized. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-09-07T00:00:00Z 2018-09-07 2020-12-01T00:00:00Z |
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/10773/24082 |
url |
http://hdl.handle.net/10773/24082 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
0024-3795 10.1016/j.laa.2018.08.024 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/embargoedAccess |
eu_rights_str_mv |
embargoedAccess |
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 |
mluisa.alvim@gmail.com |
_version_ |
1817543686876037120 |