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Article overview
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Orbigraphs: a graph theoretic analog to Riemannian orbifolds | | Kathleen Daly
; Colin Gavin
; Gabriel Montes de Oca
; Diana Ochoa
; Elizabeth Stanhope
; Sam Stewart
; | | Date: |
11 Jan 2019 | | Abstract: | A Riemannian orbifold is a mildly singular generalization of a Riemannian
manifold that is locally modeled on $R^n$ modulo the action of a finite group.
Orbifolds have proven interesting in a variety of settings. Spectral geometers
have examined the link between the Laplace spectrum of an orbifold and the
singularities of the orbifold. One open question in this field is whether or
not a singular orbifold and a manifold can be Laplace isospectral. Motivated by
the connection between spectral geometry and spectral graph theory, we define a
graph theoretic analogue of an orbifold called an orbigraph. We obtain results
about the relationship between an orbigraph and the spectrum of its adjacency
matrix. We prove that the number of singular vertices present in an orbigraph
is bounded above and below by spectrally determined quantities, and show that
an orbigraph with a singular point and a regular graph cannot be cospectral. We
also provide a lower bound on the Cheeger constant of an orbigraph. | | Source: | arXiv, 1901.3743 | | Services: | Forum | Review | PDF | Favorites | |
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