{
  "id": "1312.4096",
  "version": "v1",
  "published": "2013-12-15T01:04:34.000Z",
  "updated": "2013-12-15T01:04:34.000Z",
  "title": "A Simple Proof of the Cayley Formula using Random Graphs",
  "authors": [
    "Scott Wu",
    "Ray Li",
    "Andrew He",
    "Steven Hao"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We present a nice result on the probability of a cycle occurring in a randomly generated graph. We then provide some extensions and applications, including the proof of the famous Cayley formula, which states that the number of labeled trees on $n$ vertices is $n^{n-2}.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-15T01:04:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C80",
      "05C05",
      "05C38"
    ],
    "keywords": [
      "random graphs",
      "simple proof",
      "nice result",
      "famous cayley formula",
      "probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.4096W"
    }
  }
}