{
  "id": "1709.09011",
  "version": "v1",
  "published": "2017-09-26T13:41:06.000Z",
  "updated": "2017-09-26T13:41:06.000Z",
  "title": "The smallest eigenvalues of Hamming graphs, Johnson graphs and other distance-regular graphs with classical parameters",
  "authors": [
    "Andries E. Brouwer",
    "Sebastian M. Cioabă",
    "Ferdinand Ihringer",
    "Matt McGinnis"
  ],
  "comment": "29 pages",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "We prove a conjecture by Van Dam and Sotirov on the smallest eigenvalue of (distance-$j$) Hamming graphs and a conjecture by Karloff on the smallest eigenvalue of (distance-$j$) Johnson graphs. More generally, we study the smallest eigenvalue and the second largest eigenvalue in absolute value of the graphs of the relations of classical $P$- and $Q$-polynomial association schemes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-26T13:41:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smallest eigenvalue",
      "johnson graphs",
      "hamming graphs",
      "distance-regular graphs",
      "classical parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}