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 als...

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Detalles Bibliográficos
Autores: Durand-Cartagena, Estibalitz, Soria de Diego, Francisco Javier, Tradacete Pérez, Pedro
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/105183
Acceso en línea:https://hdl.handle.net/20.500.14352/105183
Access Level:acceso abierto
Palabra clave:Doubling measure
Infinite graph
Spectral graph theory
Matemáticas (Matemáticas)
12 Matemáticas
Descripción
Sumario: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.