{
  "id": "0905.3268",
  "version": "v1",
  "published": "2009-05-20T10:13:34.000Z",
  "updated": "2009-05-20T10:13:34.000Z",
  "title": "Dominating sets and Domination polynomials of Cycles",
  "authors": [
    "Saeid Alikhani",
    "Yee-hock Peng"
  ],
  "comment": "13 pages. Accepted in http://www.ripublication.com/gjpam.htm",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let G=(V,E) be a simple graph. A set S\\subset V is a dominating set of G, if every vertex in V\\S is adjacent to at least one vertex in S. Let {\\mathcal C}_n^i be the family of dominating sets of a cycle C_n with cardinality i, and let d(C_n,i) = |{\\mathcal C}_n^i. In this paper, we construct {\\mathcal C}_n^i, and obtain a recursive formula for d(C_n, i). Using this recursive formula, we consider the polynomial D(C_n, x) = \\sum_{i=1}^n d(C_n, i)x^i, which we call domination polynomial of cycles and obtain some properties of this polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-20T10:13:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "11B83"
    ],
    "keywords": [
      "dominating set",
      "domination polynomial",
      "recursive formula",
      "simple graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.3268A"
    }
  }
}