{
  "id": "0904.4819",
  "version": "v1",
  "published": "2009-04-30T13:12:01.000Z",
  "updated": "2009-04-30T13:12:01.000Z",
  "title": "The independence polynomial of a graph at -1",
  "authors": [
    "Vadim E. Levit",
    "Eugen Mandrescu"
  ],
  "comment": "16 pages; 13 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "If alpha=alpha(G) is the maximum size of an independent set and s_{k} equals the number of stable sets of cardinality k in graph G, then I(G;x)=s_{0}+s_{1}x+...+s_{alpha}x^{alpha} is the independence polynomial of G. In this paper we prove that: 1. I(T;-1) equels either -1 or 0 or 1 for every tree T; 2. I(G;-1)=0 for every connected well-covered graph G of girth > 5, non-isomorphic to C_{7} or K_{2}; 3. the absolute value of I(G;-1) is not greater than 2^nu(G), for every graph G, where nu(G) is its cyclomatic number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-04-30T13:12:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05A20",
      "05C05"
    ],
    "keywords": [
      "independence polynomial",
      "absolute value",
      "cyclomatic number",
      "independent set",
      "cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0904.4819L"
    }
  }
}