Doubling constants and spectral theory on graphs
Combinatorics
2021-11-18 v1 Metric Geometry
Abstract
We study the least doubling constant among all possible doubling measures defined on a (finite or infinite) graph . We show that this constant can be estimated from below by , where is the spectral radius of the adjacency matrix of , 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.
Cite
@article{arxiv.2111.09199,
title = {Doubling constants and spectral theory on graphs},
author = {Estibalitz Durand-Cartagena and Javier Soria and Pedro Tradacete},
journal= {arXiv preprint arXiv:2111.09199},
year = {2021}
}