Durand Cartagena, EstibalitzSoria, JavierTradacete, Pedro2024-12-022024-12-022023-02-08Estibalitz 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.2023.113354.2578-9252https://doi.org/10.1016/j.disc.2023.113354https://hdl.handle.net/20.500.14468/24655The 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.2023.113354La 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.2023.113354We 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.esinfo:eu-repo/semantics/openAccess12 Matemáticasartículodoubling measureinfinite graphspectral graph theory