%0 Journal Article
%A Durand-Cartagena, Estibalitz
%A Soria de Diego, Francisco Javier
%A Tradacete Pérez, Pedro
%T Doubling constants and spectral theory on graphs
%D 2023
%U https://hdl.handle.net/20.500.14352/105183
%X 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.
%~