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Trivalent expanders, $(Delta – Y)$-transformation, and hyperbolic surfaces

Ivrissimtzis, Ioannis; Peyerimhoff, Norbert; Vdovina, Alina

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Authors

Alina Vdovina



Abstract

We construct a new family of trivalent expanders tessellating hyperbolic surfaces with large isometry groups. These graphs are obtained from a family of Cayley graphs of nilpotent groups via (Delta–Y)-transformations. We study combinatorial, topological and spectral properties of our trivalent graphs and their associated hyperbolic surfaces. We compare this family with Platonic graphs and their associated hyperbolic surfaces and see that they are generally very different with only one hyperbolic surface in the intersection. Finally, we provide a number theory free proof of the Ramanujan property for Platonic graphs and a special family of subgraphs.

Journal Article Type Article
Online Publication Date Jul 1, 2019
Publication Date Jul 1, 2019
Deposit Date Aug 8, 2019
Publicly Available Date Jul 1, 2020
Journal Groups, Geometry, and Dynamics
Print ISSN 1661-7207
Publisher EMS Press
Peer Reviewed Peer Reviewed
Volume 13
Issue 3
Pages 1103-1131
DOI https://doi.org/10.4171/ggd/518
Public URL https://durham-repository.worktribe.com/output/1295607

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