{
  "id": "1204.4580",
  "version": "v1",
  "published": "2012-04-20T10:44:33.000Z",
  "updated": "2012-04-20T10:44:33.000Z",
  "title": "The number of graphs of given diameter",
  "authors": [
    "Zoltan Furedi",
    "Younjin Kim"
  ],
  "comment": "13 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper it is proved that there are constants 0< c_2< c_1 such that an asymptotic formula can be given for the the number of (labeled) n-vertex graphs of diameter d whenever n tends to infinity and 2 < d < n - c_1 (log n). A typical graph of diameter d consists of a combination of an induced path of length d and a highly connected block of size n-d+3. In the case d > n- c_2(log n) another asymptotic formula is calculated and the typical graph has a completely different snakelike structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-20T10:44:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "05C80"
    ],
    "keywords": [
      "asymptotic formula",
      "typical graph",
      "snakelike structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.4580F"
    }
  }
}