Analysis & Applications Seminar

Least doubling constants on graphs and spectral theory

Speaker:  Javier Soria (Universidad Complutense de Madrid )
Date:  Friday, 20 May 2022 - 11:30
Place:  Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Online: (ID: 817 1460 0792)


We study the least doubling constant \(C_G\) among all possible doubling measures defined on a graph \(G\). In particular, for a path graph \(G=L_n\),  we show that  \(1+2\cos(\frac{\pi}{n+1})\leq C_{L_n}<3\), with equality on the lower bound if and only if \(n\le8\). 
We then prove  that \(C_G\), for a general graph \(G\), can be estimated from below by  \( 1+ r(A_G) \), where \(r(A_G) \) is the spectral radius of the adjacency matrix of  \(G\), and study when both quantities coincide. 
Finally, we give a complete characterization of graphs with doubling constant smaller than 3, in the spirit of Smith graphs.
This is a joint work with E. Durand-Cartagena (UNED) and P. Tradacete (CSIC).