{
  "id": "1503.01900",
  "version": "v1",
  "published": "2015-03-06T10:30:16.000Z",
  "updated": "2015-03-06T10:30:16.000Z",
  "title": "On the anti-forcing number of fullerene graphs",
  "authors": [
    "Qin Yang",
    "Heping Zhang",
    "Yuqing Lin"
  ],
  "comment": "18 pages, 12 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The anti-forcing number of a connected graph $G$ is the smallest number of edges such that the remaining graph obtained by deleting these edges has a unique perfect matching. In this paper, we show that the anti-forcing number of every fullerene has at least four. We give a procedure to construct all fullerenes whose anti-forcing numbers achieve the lower bound four. Furthermore, we show that, for every even $n\\geq20$ ($n\\neq22,26$), there exists a fullerene with $n$ vertices that has the anti-forcing number four, and the fullerene with 26 vertices has the anti-forcing number five.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-06T10:30:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C70",
      "92E10"
    ],
    "keywords": [
      "fullerene graphs",
      "smallest number",
      "anti-forcing numbers achieve",
      "lower bound",
      "unique perfect matching"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}