Skip to main content

Research Repository

Advanced Search

On the local geometry of graphs in terms of their spectra

Huang, Brice; Rahman, Mustazee

On the local geometry of graphs in terms of their spectra Thumbnail


Authors

Brice Huang



Abstract

In this paper we consider the relation between the spectrum and the number of short cycles in large graphs. Suppose G1,G2,G3,... is a sequence of finite and connected graphs that share a common universal cover T and such that the proportion of eigenvalues of Gn that lie within the support of the spectrum of T tends to 1 in the large limit. This is a weak notion of being Ramanujan. We prove such a sequence of graphs is asymptotically locally tree-like. This is deduced by way of an analogous theorem proved for certain infinite sofic graphs and unimodular networks, which extends results for regular graphs and certain infinite Cayley graphs.

Citation

Huang, B., & Rahman, M. (2019). On the local geometry of graphs in terms of their spectra. European Journal of Combinatorics, 81, 378-393. https://doi.org/10.1016/j.ejc.2019.07.001

Journal Article Type Article
Acceptance Date Jul 3, 2019
Online Publication Date Jul 10, 2019
Publication Date 2019-10
Deposit Date Sep 25, 2019
Publicly Available Date Oct 6, 2021
Journal European Journal of Combinatorics
Print ISSN 0195-6698
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 81
Pages 378-393
DOI https://doi.org/10.1016/j.ejc.2019.07.001

Files




You might also like



Downloadable Citations