Durand-Cartagena, EstibalitzSoria de Diego, Francisco JavierTradacete Pérez, Pedro2024-06-212024-06-21202310.1016/j.disc.2023.113354https://hdl.handle.net/20.500.14352/105183We 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.engAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/journal articlehttps://doi.org/10.1016/j.disc.2023.113354open accessDoubling measureInfinite graphSpectral graph theoryMatemáticas (Matemáticas)12 Matemáticas