Partial characterization of graphs having a single large Laplacian eigenvalue

Autores
Allem, L. Emilio; Grippo, Luciano Norberto; Cafure, Antonio; Dratman, Ezequiel; Safe, Martín D.; Trevisan, Vilmar
Año de publicación
2018
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Safe, Martín M. Universidad Nacional del Sur. Departamento de Matemática; Argentina.
Fil: Allem, L. Emilio. Universidade Federal do Rio Grande do Sul. Instituto de Matemática; Brazil.
Fil: Cafure, Antonio. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina.
Fil: Trevisan, Vilmar. Universidade Federal do Rio Grande do Sul; Brasil.
Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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.
Fuente
The Electronic Journal of Combinatorics. 12-2018; 25(4): 4-65
https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p65/pdf
Materia
Laplacian Matrix
Graphs
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/4.0/
Repositorio
Repositorio Institucional UNGS
Institución
Universidad Nacional de General Sarmiento
OAI Identificador
oai:repositorio.ungs.edu.ar:UNGS/1587
Acceder
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oai_identifier_str oai:repositorio.ungs.edu.ar:UNGS/1587
network_acronym_str RIUNGS
repository_id_str
network_name_str Repositorio Institucional UNGS
spelling Partial characterization of graphs having a single large Laplacian eigenvalueAllem, L. EmilioGrippo, Luciano NorbertoCafure, AntonioDratman, EzequielSafe, Martín D.Trevisan, VilmarLaplacian MatrixGraphsFil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.Fil: Safe, Martín M. Universidad Nacional del Sur. Departamento de Matemática; Argentina.Fil: Allem, L. Emilio. Universidade Federal do Rio Grande do Sul. Instituto de Matemática; Brazil.Fil: Cafure, Antonio. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina.Fil: Trevisan, Vilmar. Universidade Federal do Rio Grande do Sul; Brasil.Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.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.The Electronic Journal of Combinatorics2024-07-16T17:07:07Z2024-07-16T17:07:07Z2018info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfAllem, L. E et al. (12-2018). Partial characterization of graphs having a single large Laplacian eigenvalue. The Electronic Journal of Combinatorics, 25(4), 4-65.1077-8926http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1587The Electronic Journal of Combinatorics. 12-2018; 25(4): 4-65https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p65/pdfreponame:Repositorio Institucional UNGSinstname:Universidad Nacional de General Sarmientoenginfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/4.0/2025-10-30T12:35:16Zoai:repositorio.ungs.edu.ar:UNGS/1587instacron:UNGSInstitucionalhttp://repositorio.ungs.edu.ar:8080/Universidad públicahttps://www.ungs.edu.ar/http://repositorio.ungs.edu.ar:8080/oaiubyd@campus.ungs.edu.arArgentinaopendoar:2025-10-30 12:35:16.637Repositorio Institucional UNGS - Universidad Nacional de General Sarmientofalse
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
Grippo, Luciano Norberto
Cafure, Antonio
Dratman, Ezequiel
Safe, Martín D.
Trevisan, Vilmar
author Allem, L. Emilio
author_facet Allem, L. Emilio
Grippo, Luciano Norberto
Cafure, Antonio
Dratman, Ezequiel
Safe, Martín D.
Trevisan, Vilmar
author_role author
author2 Grippo, Luciano Norberto
Cafure, Antonio
Dratman, Ezequiel
Safe, Martín D.
Trevisan, Vilmar
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv Laplacian Matrix
Graphs
topic Laplacian Matrix
Graphs
dc.description.none.fl_txt_mv Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
Fil: Safe, Martín M. Universidad Nacional del Sur. Departamento de Matemática; Argentina.
Fil: Allem, L. Emilio. Universidade Federal do Rio Grande do Sul. Instituto de Matemática; Brazil.
Fil: Cafure, Antonio. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina.
Fil: Trevisan, Vilmar. Universidade Federal do Rio Grande do Sul; Brasil.
Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
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.
description Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
publishDate 2018
dc.date.none.fl_str_mv 2018
2024-07-16T17:07:07Z
2024-07-16T17:07:07Z
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 Allem, L. E et al. (12-2018). Partial characterization of graphs having a single large Laplacian eigenvalue. The Electronic Journal of Combinatorics, 25(4), 4-65.
1077-8926
http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1587
identifier_str_mv Allem, L. E et al. (12-2018). Partial characterization of graphs having a single large Laplacian eigenvalue. The Electronic Journal of Combinatorics, 25(4), 4-65.
1077-8926
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1587
dc.language.none.fl_str_mv eng
language eng
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv The Electronic Journal of Combinatorics
publisher.none.fl_str_mv The Electronic Journal of Combinatorics
dc.source.none.fl_str_mv The Electronic Journal of Combinatorics. 12-2018; 25(4): 4-65
https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p65/pdf
reponame:Repositorio Institucional UNGS
instname:Universidad Nacional de General Sarmiento
reponame_str Repositorio Institucional UNGS
collection Repositorio Institucional UNGS
instname_str Universidad Nacional de General Sarmiento
repository.name.fl_str_mv Repositorio Institucional UNGS - Universidad Nacional de General Sarmiento
repository.mail.fl_str_mv ubyd@campus.ungs.edu.ar
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score 12.589754

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