{
  "id": "1206.5926",
  "version": "v2",
  "published": "2012-06-26T08:58:50.000Z",
  "updated": "2012-09-18T01:29:44.000Z",
  "title": "Recurrence relations and splitting formulas for the domination polynomial",
  "authors": [
    "Tomer Kotek",
    "James Preen",
    "Frank Simon",
    "Peter Tittmann",
    "Martin Trinks"
  ],
  "journal": "The Electronic Journal of Combinatorics 19(3) (2012) #P47",
  "categories": [
    "math.CO"
  ],
  "abstract": "The domination polynomial D(G,x) of a graph G is the generating function of its dominating sets. We prove that D(G,x) satisfies a wide range of reduction formulas. We show linear recurrence relations for D(G,x) for arbitrary graphs and for various special cases. We give splitting formulas for D(G,x) based on articulation vertices, and more generally, on splitting sets of vertices.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-18T01:29:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C31"
    ],
    "keywords": [
      "domination polynomial",
      "splitting formulas",
      "linear recurrence relations",
      "articulation vertices",
      "special cases"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.5926K"
    }
  }
}