Partial characterization of graphs having a single large Laplacian eigenvalue

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dc.creator Allem, L. Emilio
dc.creator Grippo, Luciano Norberto
dc.creator Cafure, Antonio
dc.creator Dratman, Ezequiel
dc.creator Safe, Martín D.
dc.creator Trevisan, Vilmar
dc.date.accessioned 2024-07-16T17:07:07Z
dc.date.available 2024-07-16T17:07:07Z
dc.date.issued 2018
dc.identifier.citation 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.
dc.identifier.issn 1077-8926
dc.identifier.uri http://repositorio.ungs.edu.ar:8080/xmlui/handle/UNGS/1587
dc.description Fil: Grippo, Luciano Norberto. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
dc.description Fil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina.
dc.description Fil: Safe, Martín M. Universidad Nacional del Sur. Departamento de Matemática; Argentina.
dc.description Fil: Allem, L. Emilio. Universidade Federal do Rio Grande do Sul. Instituto de Matemática; Brazil.
dc.description Fil: Cafure, Antonio. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina.
dc.description Fil: Trevisan, Vilmar. Universidade Federal do Rio Grande do Sul; Brasil.
dc.description Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina.
dc.description.abstract 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.
dc.format application/pdf
dc.language eng
dc.publisher The Electronic Journal of Combinatorics
dc.rights info:eu-repo/semantics/openAccess
dc.rights https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.source The Electronic Journal of Combinatorics. 12-2018; 25(4): 4-65
dc.source.uri https://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i4p65/pdf
dc.subject Laplacian Matrix
dc.subject Graphs
dc.title Partial characterization of graphs having a single large Laplacian eigenvalue
dc.type info:eu-repo/semantics/article
dc.type info:ar-repo/semantics/artículo
dc.type info:eu-repo/semantics/publishedVersion


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