Mirror graphs: graph theoretical characterization of reflection arrangements and finite Coxeter groups
Combinatorics
2016-09-05 v1 Discrete Mathematics
Abstract
Mirror graphs were introduced by Bre\v{s}ar et al. in 2004 as an intriguing class of graphs: vertex-transitive, isometrically embeddable into hypercubes, having a strong connection with regular maps and polytope structure. In this article we settle the structure of mirror graphs by characterizing them as precisely the Cayley graphs of the finite Coxeter groups or equivalently the tope graphs of reflection arrangements - well understood and classified structures. We provide a polynomial algorithm for their recognition.
Keywords
Cite
@article{arxiv.1609.00591,
title = {Mirror graphs: graph theoretical characterization of reflection arrangements and finite Coxeter groups},
author = {Tilen Marc},
journal= {arXiv preprint arXiv:1609.00591},
year = {2016}
}