{
  "id": "0908.2017",
  "version": "v1",
  "published": "2009-08-14T06:42:34.000Z",
  "updated": "2009-08-14T06:42:34.000Z",
  "title": "On Distance-Regular Graphs with Smallest Eigenvalue at Least $-m$",
  "authors": [
    "J. H. Koolen",
    "S. Bang"
  ],
  "categories": [
    "math.CO",
    "math.SP"
  ],
  "abstract": "A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer $m\\geq 2$, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least $-m$, diameter at least three and intersection number $c_2 \\geq 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-08-14T06:42:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C75",
      "05E30"
    ],
    "keywords": [
      "smallest eigenvalue",
      "non-complete geometric distance-regular graph",
      "non-geometric distance-regular graphs",
      "partial geometry",
      "intersection number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2017K"
    }
  }
}