Partial Characterization of Graphs Having a Single Large Laplacian Eigenvalue

Autores
Allem, L. Emilio; Cafure, Antonio Artemio; Dratman, Ezequiel; Grippo, Luciano Norberto; Safe, Martin Dario; Trevisan, Vilmar
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The parameter σ(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 σ(G) = 1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between σ(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.
Fil: Allem, L. Emilio. Universidade Federal do Rio Grande do Sul; Brasil
Fil: Cafure, Antonio Artemio. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Safe, Martin Dario. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Trevisan, Vilmar. Universidade Federal do Rio Grande do Sul; Brasil
Materia
Laplacian Matrix
Graphs
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/104147
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/104147
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Partial Characterization of Graphs Having a Single Large Laplacian EigenvalueAllem, L. EmilioCafure, Antonio ArtemioDratman, EzequielGrippo, Luciano NorbertoSafe, Martin DarioTrevisan, VilmarLaplacian MatrixGraphshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The parameter σ(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 σ(G) = 1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between σ(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.Fil: Allem, L. Emilio. Universidade Federal do Rio Grande do Sul; BrasilFil: Cafure, Antonio Artemio. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Safe, Martin Dario. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Trevisan, Vilmar. Universidade Federal do Rio Grande do Sul; BrasilElectronic Journal Of Combinatorics2018-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/104147Allem, L. Emilio; Cafure, Antonio Artemio; Dratman, Ezequiel; Grippo, Luciano Norberto; Safe, Martin Dario; et al.; Partial Characterization of Graphs Having a Single Large Laplacian Eigenvalue; Electronic Journal Of Combinatorics; Electronic Journal Of Combinatorics, The; 25; 4; 12-2018; 1-101077-8926CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p65info:eu-repo/semantics/altIdentifier/doi/10.37236/7342info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-29T12:25:43Zoai:ri.conicet.gov.ar:11336/104147instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-29 12:25:43.737CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.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, L. Emilio
Laplacian Matrix
Graphs
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
dc.creator.none.fl_str_mv Allem, L. Emilio
Cafure, Antonio Artemio
Dratman, Ezequiel
Grippo, Luciano Norberto
Safe, Martin Dario
Trevisan, Vilmar
author Allem, L. Emilio
author_facet Allem, L. Emilio
Cafure, Antonio Artemio
Dratman, Ezequiel
Grippo, Luciano Norberto
Safe, Martin Dario
Trevisan, Vilmar
author_role author
author2 Cafure, Antonio Artemio
Dratman, Ezequiel
Grippo, Luciano Norberto
Safe, Martin Dario
Trevisan, Vilmar
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Laplacian Matrix
Graphs
topic Laplacian Matrix
Graphs
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The parameter σ(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 σ(G) = 1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between σ(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.
Fil: Allem, L. Emilio. Universidade Federal do Rio Grande do Sul; Brasil
Fil: Cafure, Antonio Artemio. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Safe, Martin Dario. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Trevisan, Vilmar. Universidade Federal do Rio Grande do Sul; Brasil
description The parameter σ(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 σ(G) = 1. Our conjecture is that these graphs are stars plus a (possible empty) set of isolated vertices. We establish a link between σ(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.none.fl_str_mv 2018-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/104147
Allem, L. Emilio; Cafure, Antonio Artemio; Dratman, Ezequiel; Grippo, Luciano Norberto; Safe, Martin Dario; et al.; Partial Characterization of Graphs Having a Single Large Laplacian Eigenvalue; Electronic Journal Of Combinatorics; Electronic Journal Of Combinatorics, The; 25; 4; 12-2018; 1-10
1077-8926
CONICET Digital
CONICET
url http://hdl.handle.net/11336/104147
identifier_str_mv Allem, L. Emilio; Cafure, Antonio Artemio; Dratman, Ezequiel; Grippo, Luciano Norberto; Safe, Martin Dario; et al.; Partial Characterization of Graphs Having a Single Large Laplacian Eigenvalue; Electronic Journal Of Combinatorics; Electronic Journal Of Combinatorics, The; 25; 4; 12-2018; 1-10
1077-8926
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p65
info:eu-repo/semantics/altIdentifier/doi/10.37236/7342
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Electronic Journal Of Combinatorics
publisher.none.fl_str_mv Electronic Journal Of Combinatorics
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1847427169531199488
score 12.589754

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