Doubling constants and spectral theory on graphs

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 il...

ver descrição completa

Detalhes bibliográficos
Autores: Durand Cartagena, Estibalitz, Soria, Javier, Tradacete, Pedro
Formato: artículo
Fecha de publicación:2023
País:España
Recursos:Universidad Nacional de Educación a Distancia
Repositorio:e-spacio. Repositorio Institucional de la UNED
Idioma:español
OAI Identifier:oai:e-spacio.uned.es:20.500.14468/24655
Acesso em linha:https://hdl.handle.net/20.500.14468/24655
Access Level:acceso abierto
Palavra-chave:12 Matemáticas
doubling measure
infinite graph
spectral graph theory
Descrição
Resumo: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.