Publication: Doubling constants and spectral theory on graphs
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Date
2023-02-08
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info:eu-repo/semantics/openAccess
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Elsevier
Abstract
We study the least doubling constant among all possible doubling measures defined on a (finite or infinite) graph G. We show that this constant can be estimated from below by 1+r(AG), where r(AG) is the spectral radius of the adjacency matrix of G, and study when both quantities coincide. We also illustrate how amenability of the automorphism group of a graph can be related to finding doubling minimizers. Finally, we give a complete characterization of graphs with doubling constant smaller than 3, in the spirit of Smith graphs.
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The registered version of this article, first published in Discrete Mathematics, is available online at the publisher's website: Elsevier, https://doi.org/10.1016/j.disc.2023.113354
La versión registrada de este artículo, publicado por primera vez en Discrete Mathematics, está disponible en línea en el sitio web del editor: Elsevier, https://doi.org/10.1016/j.disc.2023.113354
La versión registrada de este artículo, publicado por primera vez en Discrete Mathematics, está disponible en línea en el sitio web del editor: Elsevier, https://doi.org/10.1016/j.disc.2023.113354
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Keywords
doubling measure, infinite graph, spectral graph theory
Citation
Estibalitz Durand-Cartagena, Javier Soria, Pedro Tradacete, Doubling constants and spectral theory on graphs, Discrete Mathematics, Volume 346, Issue 6, 2023, 113354, ISSN 0012-365X, https://doi.org/10.1016/j.disc.2023.113354.
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Facultades y escuelas::E.T.S. de Ingenieros Industriales
Department
Matemática Aplicada I