{
  "id": "0906.2809",
  "version": "v2",
  "published": "2009-06-15T21:54:50.000Z",
  "updated": "2010-04-06T20:27:26.000Z",
  "title": "Sandpile groups and spanning trees of directed line graphs",
  "authors": [
    "Lionel Levine"
  ],
  "comment": "v2 has an expanded section on deletion/contraction for directed graphs, and a more detailed proof of Theorem 2.3. To appear in Journal of Combinatorial Theory A.",
  "doi": "10.1016/j.jcta.2010.04.001",
  "categories": [
    "math.CO"
  ],
  "abstract": "We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associated to a directed graph, whose order is the number of oriented spanning trees rooted at a fixed vertex. In the case when G is regular of degree k, we show that the sandpile group of G is isomorphic to the quotient of the sandpile group of LG by its k-torsion subgroup. As a corollary we compute the sandpile groups of two families of graphs widely studied in computer science, the de Bruijn graphs and Kautz graphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-04-06T20:27:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C20",
      "05C25",
      "05C50"
    ],
    "keywords": [
      "sandpile group",
      "oriented spanning trees",
      "directed line graph lg",
      "directed graph",
      "computer science"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2809L"
    }
  }
}