Trivalent expanders, $(\Delta-Y)$-transformation, and hyperbolic surfaces
Combinatorics
2018-10-15 v1
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 -transformations. 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. Moreover, we study combinatorial, topological and spectral properties of our trivalent graphs and their associated hyperbolic surfaces.
Cite
@article{arxiv.1810.05532,
title = {Trivalent expanders, $(\Delta-Y)$-transformation, and hyperbolic surfaces},
author = {Ioannis Ivrissimtzis and Norbert Peyerimhoff and Alina Vdovina},
journal= {arXiv preprint arXiv:1810.05532},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1202.2304