Trivalent expanders and hyperbolic surfaces
Ioannis Ivrissimtzis, Norbert Peyerimhoff, Alina Vdovina
TL;DR
This paper introduces a new family of trivalent expander graphs that tessellate compact hyperbolic surfaces, analyzing their topological and spectral properties and comparing them with existing Platonic graphs.
Contribution
It presents a novel family of trivalent expanders that tessellate hyperbolic surfaces, expanding the understanding of their topological and spectral characteristics.
Findings
The new expanders tessellate compact hyperbolic surfaces.
They have large isometry groups.
Spectral properties are characterized and compared with Platonic graphs.
Abstract
We introduce a family of trivalent expanders which tessellate compact hyperbolic surfaces with large isometry groups. We compare this family with Platonic graphs and modifications of them and prove topological and spectral properties of these families.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Algebraic Geometry and Number Theory