{
  "id": "0712.3895",
  "version": "v1",
  "published": "2007-12-23T05:29:02.000Z",
  "updated": "2007-12-23T05:29:02.000Z",
  "title": "An Enumeration of Graphical Designs",
  "authors": [
    "Yeow Meng Chee",
    "Petteri Kaski"
  ],
  "comment": "16 pages",
  "journal": "Journal of Combinatorial Designs, vol. 16, no. 1, pp. 70-85, 2008",
  "doi": "10.1002/jcd.20137",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\Psi(t,k)$ denote the set of pairs $(v,\\lambda)$ for which there exists a graphical $t$-$(v,k,\\lambda)$ design. Most results on graphical designs have gone to show the finiteness of $\\Psi(t,k)$ when $t$ and $k$ satisfy certain conditions. The exact determination of $\\Psi(t,k)$ for specified $t$ and $k$ is a hard problem and only $\\Psi(2,3)$, $\\Psi(2,4)$, $\\Psi(3,4)$, $\\Psi(4,5)$, and $\\Psi(5,6)$ have been determined. In this paper, we determine completely the sets $\\Psi(2,5)$ and $\\Psi(3,5)$. As a result, we find more than 270000 inequivalent graphical designs, and more than 8000 new parameter sets for which there exists a graphical design. Prior to this, graphical designs are known for only 574 parameter sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-12-23T05:29:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parameter sets",
      "enumeration",
      "hard problem",
      "inequivalent graphical designs",
      "exact determination"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3895M"
    }
  }
}