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...
| Autores: | , , |
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| 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 |
| 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. |
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