Semisymmetric Graphs from Polytopes
Combinatorics
2007-05-23 v1 Metric Geometry
Abstract
Every finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain a construction for semisymmetric trivalent graphs (which are edge- but not vertex-transitive). In particular, the Gray graph arises as the medial layer graph of a certain universal locally toroidal regular 4-polytope.
Keywords
Cite
@article{arxiv.math/0606469,
title = {Semisymmetric Graphs from Polytopes},
author = {Barry Monson and Tomaz Pisanski and Egon Schulte and Asia Ivic Weiss},
journal= {arXiv preprint arXiv:math/0606469},
year = {2007}
}
Comments
18 pages (to appear in Journal Combinatorial Theory, Series A)