{
  "id": "math/0606163",
  "version": "v1",
  "published": "2006-06-07T17:48:48.000Z",
  "updated": "2006-06-07T17:48:48.000Z",
  "title": "On the Enumeration of Certain Weighted Graphs",
  "authors": [
    "Miklós Bóna",
    "Hyeong-Kwan Ju",
    "Ruriko Yoshida"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We enumerate weighted graphs with a certain upper bound condition. We also compute the generating function of the numbers of these graphs, and prove that it is a rational function. In particular, we show that if the given graph is a bipartite graph, then its generating function is of the form $\\frac{p(x)}{(1-x)^{m+1}}$, where $m$ is the number of vertices of the graph and $p(x)$ is a polynomial of degree at most $m$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-07T17:48:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "enumeration",
      "generating function",
      "upper bound condition",
      "enumerate weighted graphs",
      "rational function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6163B"
    }
  }
}