{
  "id": "1101.0440",
  "version": "v1",
  "published": "2011-01-03T00:18:19.000Z",
  "updated": "2011-01-03T00:18:19.000Z",
  "title": "Geometric distance-regular graphs without 4-claws",
  "authors": [
    "Sejeong Bang"
  ],
  "categories": [
    "math.CO",
    "math.SP"
  ],
  "abstract": "A non-complete \\drg $\\Gamma$ is called geometric if there exists a set $\\mathcal{C}$ of Delsarte cliques such that each edge of $\\Gamma$ lies in a unique clique in $\\mathcal{C}$. In this paper, we determine the non-complete distance-regular graphs satisfying $\\max \\{3, 8/3}(a_1+1)\\}<k<4a_1+10-6c_2$. To prove this result, we first show by considering non-existence of 4-claws that any non-complete distance-regular graph satisfying $\\max \\{3, \\8/3}(a_1+1)\\}<k<4a_1+10-6c_2$ is a geometric \\drg with smallest eigenvalue -3. Moreover, we classify the geometric \\drg s with smallest eigenvalue -3. As an application, 7 feasible intersection arrays in the list of \\cite[Chapter 14]{bcn} are ruled out.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-03T00:18:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E30",
      "05C50",
      "05C75"
    ],
    "keywords": [
      "geometric distance-regular graphs",
      "smallest eigenvalue",
      "non-complete distance-regular graph satisfying",
      "unique clique",
      "non-complete distance-regular graphs satisfying"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.0440B"
    }
  }
}