Partial characterization of graphs having a single large Laplacian eigenvalue

Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.

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Detalles Bibliográficos
Autores principales: Allem, L. Emilio, Grippo, Luciano Norberto, Cafure, Antonio, Dratman, Ezequiel, Safe, Martín D., Trevisan, Vilmar
Formato: Artículo publishedVersion
Lenguaje:Inglés
Publicado: The Electronic Journal of Combinatorics 2024
Materias:
Laplacian Matrix
Graphs
Acceso en línea:http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1587
Aporte de:
Repositorio Institucional Digital de Acceso Abierto (UNGS) de Universidad Nacional de General Sarmiento
id I71-R177-UNGS-1587
record_format dspace
spelling I71-R177-UNGS-15872024-07-16T17:13:43Z Partial characterization of graphs having a single large Laplacian eigenvalue Allem, L. Emilio Grippo, Luciano Norberto Cafure, Antonio Dratman, Ezequiel Safe, Martín D. Trevisan, Vilmar Laplacian Matrix Graphs 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. 2024-07-16T17:07:07Z 2024-07-16T17:07:07Z 2018 info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion 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 eng info:eu-repo/semantics/openAccess https://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf application/pdf The Electronic Journal of Combinatorics The Electronic Journal of Combinatorics. 12-2018; 25(4): 4-65 https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p65/pdf
institution Universidad Nacional de General Sarmiento
institution_str I-71
repository_str R-177
collection Repositorio Institucional Digital de Acceso Abierto (UNGS)
language Inglés
orig_language_str_mv eng
topic Laplacian Matrix
Graphs
spellingShingle Laplacian Matrix
Graphs
Allem, L. Emilio
Grippo, Luciano Norberto
Cafure, Antonio
Dratman, Ezequiel
Safe, Martín D.
Trevisan, Vilmar
Partial characterization of graphs having a single large Laplacian eigenvalue
topic_facet Laplacian Matrix
Graphs
description Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
format Artículo
Artículo
publishedVersion
author Allem, L. Emilio
Grippo, Luciano Norberto
Cafure, Antonio
Dratman, Ezequiel
Safe, Martín D.
Trevisan, Vilmar
author_facet Allem, L. Emilio
Grippo, Luciano Norberto
Cafure, Antonio
Dratman, Ezequiel
Safe, Martín D.
Trevisan, Vilmar
author_sort Allem, L. Emilio
title Partial characterization of graphs having a single large Laplacian eigenvalue
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
publisher The Electronic Journal of Combinatorics
publishDate 2024
url http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1587
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AT cafureantonio partialcharacterizationofgraphshavingasinglelargelaplacianeigenvalue
AT dratmanezequiel partialcharacterizationofgraphshavingasinglelargelaplacianeigenvalue
AT safemartind partialcharacterizationofgraphshavingasinglelargelaplacianeigenvalue
AT trevisanvilmar partialcharacterizationofgraphshavingasinglelargelaplacianeigenvalue
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