The Graphicahedron
Combinatorics
2009-10-21 v1 Metric Geometry
Abstract
The paper describes a construction of abstract polytopes from Cayley graphs of symmetric groups. Given any connected graph G with p vertices and q edges, we associate with G a Cayley graph of the symmetric group S_p and then construct a vertex-transitive simple polytope of rank q, called the graphicahedron, whose 1-skeleton (edge graph) is the Cayley graph. The graphicahedron of a graph G is a generalization of the well-known permutahedron; the latter is obtained when the graph is a path. We also discuss symmetry properties of the graphicahedron and determine its structure when G is small.
Keywords
Cite
@article{arxiv.0910.3908,
title = {The Graphicahedron},
author = {Gabriela Araujo-Pardo and Maria Del Rio-Francos and Mariana Lopez-Dudet and Deborah Oliveros and Egon Schulte},
journal= {arXiv preprint arXiv:0910.3908},
year = {2009}
}
Comments
21 pages (European Journal of Combinatorics, to appear)