{
  "id": "1706.03132",
  "version": "v1",
  "published": "2017-06-09T21:31:49.000Z",
  "updated": "2017-06-09T21:31:49.000Z",
  "title": "A characterization of $Q$-polynomial distance-regular graphs using the intersection numbers",
  "authors": [
    "Supalak Sumalroj"
  ],
  "comment": "15 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We consider a primitive distance-regular graph $\\Gamma$ with diameter at least $3$. We use the intersection numbers of $\\Gamma$ to find a positive semidefinite matrix $G$ with integer entries. We show that $G$ has determinant zero if and only if $\\Gamma$ is $Q$-polynomial.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-09T21:31:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30"
    ],
    "keywords": [
      "polynomial distance-regular graphs",
      "intersection numbers",
      "characterization",
      "determinant zero",
      "positive semidefinite matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}