{
  "id": "0910.3908",
  "version": "v1",
  "published": "2009-10-20T16:48:25.000Z",
  "updated": "2009-10-20T16:48:25.000Z",
  "title": "The Graphicahedron",
  "authors": [
    "Gabriela Araujo-Pardo",
    "Maria Del Rio-Francos",
    "Mariana Lopez-Dudet",
    "Deborah Oliveros",
    "Egon Schulte"
  ],
  "comment": "21 pages (European Journal of Combinatorics, to appear)",
  "categories": [
    "math.CO",
    "math.MG"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-20T16:48:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51M20",
      "05C25",
      "52B15"
    ],
    "keywords": [
      "graphicahedron",
      "cayley graph",
      "symmetric group",
      "symmetry properties",
      "abstract polytopes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.3908A"
    }
  }
}