Partial characterization of graphs having a single large Laplacian eigenvalue

Detalhes bibliográficos
Autor(a) principal: Allem, Luiz Emílio
Data de Publicação: 2018
Outros Autores: Cafure, Antonio Artemio, Dratman, Ezequiel, Grippo, Luciano Norberto, Safe, Martín Darío, Trevisan, Vilmar
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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spelling 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
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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
dc.format.none.fl_str_mv application/pdf
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institution 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
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