{
  "id": "0905.3281",
  "version": "v1",
  "published": "2009-05-20T11:16:10.000Z",
  "updated": "2009-05-20T11:16:10.000Z",
  "title": "The Domination Polynomials of Cubic graphs of order 10",
  "authors": [
    "Saieed Akbari",
    "Saeid Alikhani",
    "Yee-hock Peng"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let G be a simple graph of order n. The domination polynomial of G is the polynomial D(G,x)=\\sum_{i=\\gamma(G)}^{n} d(G,i) x^{i}, where d(G,i) is the number of dominating sets of G of size i, and \\gamma(G) is the domination number of G. In this paper we study the domination polynomials of cubic graphs of order 10. As a consequence, we show that the Petersen graph is determined uniquely by its domination polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-20T11:16:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C60"
    ],
    "keywords": [
      "domination polynomial",
      "cubic graphs",
      "domination number",
      "simple graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.3281A"
    }
  }
}