Partial characterization of graphs having a single large Laplacian eigenvalue
Autor(a) principal: | |
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Data de Publicação: | 2018 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRGS |
Texto Completo: | http://hdl.handle.net/10183/188908 |
Resumo: | The parameter (G) of a graph G stands for the number of Laplacian eigenvalues greater than or equal to the average degree of G. In this work, we address the problem of characterizing those graphs G having (G) = 1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between (G) and the number of anticomponents of G. As a by-product, we present some results which support the conjecture, by restricting our analysis to cographs, forests, and split graphs. |
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Allem, Luiz EmílioCafure, Antonio ArtemioDratman, EzequielGrippo, Luciano NorbertoSafe, Martín DaríoTrevisan, Vilmar2019-02-20T02:36:52Z20181077-8926http://hdl.handle.net/10183/188908001088424The parameter (G) of a graph G stands for the number of Laplacian eigenvalues greater than or equal to the average degree of G. In this work, we address the problem of characterizing those graphs G having (G) = 1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between (G) and the number of anticomponents of G. As a by-product, we present some results which support the conjecture, by restricting our analysis to cographs, forests, and split graphs.application/pdfengThe Electronic Journal of Combinatorics. United States. Vol. 25, n. 4, 2018, p. 1-10, P4.65GrafosMatriz laplacianaGraphsLaplacian matrixLaplacian eigenvaluesPartial characterization of graphs having a single large Laplacian eigenvalueEstrangeiroinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFRGSinstname:Universidade Federal do Rio Grande do Sul (UFRGS)instacron:UFRGSTEXT001088424.pdf.txt001088424.pdf.txtExtracted Texttext/plain24793http://www.lume.ufrgs.br/bitstream/10183/188908/2/001088424.pdf.txteaad866753fd88344cbe995a8d91c9c7MD52ORIGINAL001088424.pdfTexto completo (inglês)application/pdf256091http://www.lume.ufrgs.br/bitstream/10183/188908/1/001088424.pdf2113491ea3b5c76663f2d7e6abc9088eMD5110183/1889082023-05-24 03:27:32.969469oai:www.lume.ufrgs.br:10183/188908Repositório de PublicaçõesPUBhttps://lume.ufrgs.br/oai/requestopendoar:2023-05-24T06:27:32Repositório Institucional da UFRGS - Universidade Federal do Rio Grande do Sul (UFRGS)false |
dc.title.pt_BR.fl_str_mv |
Partial characterization of graphs having a single large Laplacian eigenvalue |
title |
Partial characterization of graphs having a single large Laplacian eigenvalue |
spellingShingle |
Partial characterization of graphs having a single large Laplacian eigenvalue Allem, Luiz Emílio Grafos Matriz laplaciana Graphs Laplacian matrix Laplacian eigenvalues |
title_short |
Partial characterization of graphs having a single large Laplacian eigenvalue |
title_full |
Partial characterization of graphs having a single large Laplacian eigenvalue |
title_fullStr |
Partial characterization of graphs having a single large Laplacian eigenvalue |
title_full_unstemmed |
Partial characterization of graphs having a single large Laplacian eigenvalue |
title_sort |
Partial characterization of graphs having a single large Laplacian eigenvalue |
author |
Allem, Luiz Emílio |
author_facet |
Allem, Luiz Emílio Cafure, Antonio Artemio Dratman, Ezequiel Grippo, Luciano Norberto Safe, Martín Darío Trevisan, Vilmar |
author_role |
author |
author2 |
Cafure, Antonio Artemio Dratman, Ezequiel Grippo, Luciano Norberto Safe, Martín Darío Trevisan, Vilmar |
author2_role |
author author author author author |
dc.contributor.author.fl_str_mv |
Allem, Luiz Emílio Cafure, Antonio Artemio Dratman, Ezequiel Grippo, Luciano Norberto Safe, Martín Darío Trevisan, Vilmar |
dc.subject.por.fl_str_mv |
Grafos Matriz laplaciana |
topic |
Grafos Matriz laplaciana Graphs Laplacian matrix Laplacian eigenvalues |
dc.subject.eng.fl_str_mv |
Graphs Laplacian matrix Laplacian eigenvalues |
description |
The parameter (G) of a graph G stands for the number of Laplacian eigenvalues greater than or equal to the average degree of G. In this work, we address the problem of characterizing those graphs G having (G) = 1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between (G) and the number of anticomponents of G. As a by-product, we present some results which support the conjecture, by restricting our analysis to cographs, forests, and split graphs. |
publishDate |
2018 |
dc.date.issued.fl_str_mv |
2018 |
dc.date.accessioned.fl_str_mv |
2019-02-20T02:36:52Z |
dc.type.driver.fl_str_mv |
Estrangeiro info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10183/188908 |
dc.identifier.issn.pt_BR.fl_str_mv |
1077-8926 |
dc.identifier.nrb.pt_BR.fl_str_mv |
001088424 |
identifier_str_mv |
1077-8926 001088424 |
url |
http://hdl.handle.net/10183/188908 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.ispartof.pt_BR.fl_str_mv |
The Electronic Journal of Combinatorics. United States. Vol. 25, n. 4, 2018, p. 1-10, P4.65 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
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application/pdf |
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UFRGS |
reponame_str |
Repositório Institucional da UFRGS |
collection |
Repositório Institucional da UFRGS |
bitstream.url.fl_str_mv |
http://www.lume.ufrgs.br/bitstream/10183/188908/2/001088424.pdf.txt http://www.lume.ufrgs.br/bitstream/10183/188908/1/001088424.pdf |
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