{
  "id": "1612.00007",
  "version": "v1",
  "published": "2016-11-30T21:00:00.000Z",
  "updated": "2016-11-30T21:00:00.000Z",
  "title": "On the number of maximum independent sets in Doob graphs",
  "authors": [
    "Denis Krotov"
  ],
  "comment": "5 pages, 2 figures",
  "journal": "Sib. Elektron. Mat. Izv. (Siberian Electronic Mathematical Reports) 12, 2015, 508-512",
  "doi": "10.17377/semi.2015.12.043",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The Doob graph $D(m,n)$ is a distance-regular graph with the same parameters as the Hamming graph $H(2m+n,4)$. The maximum independent sets in the Doob graphs are analogs of the distance-$2$ MDS codes in the Hamming graphs. We prove that the logarithm of the number of the maximum independent sets in $D(m,n)$ grows as $2^{2m+n-1}(1+o(1))$. The main tool for the upper estimation is constructing an injective map from the class of maximum independent sets in $D(m,n)$ to the class of distance-$2$ MDS codes in $H(2m+n,4)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-30T21:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B15",
      "05E30"
    ],
    "keywords": [
      "maximum independent sets",
      "doob graph",
      "mds codes",
      "hamming graph",
      "main tool"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}