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...
| Autores: | , , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | 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 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/24655 |
| Access Level: | acceso abierto |
| Palabra clave: | 12 Matemáticas doubling measure infinite graph spectral graph theory |
| 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. |
|---|