{
  "id": "2003.10956",
  "version": "v1",
  "published": "2020-03-24T16:31:42.000Z",
  "updated": "2020-03-24T16:31:42.000Z",
  "title": "Equitable 2-partitions of Johnson graphs with the second eigenvalue",
  "authors": [
    "Konstantin Vorob'ev"
  ],
  "comment": "16 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We study equitable 2-partitions of the Johnson graphs J(n,w) with a quotient matrix containing the eigenvalue lambda_2(w,n) = (w-2)(n-w-2)-2 in its spectrum. For any w>=4 and n>=2w, we find all admissible quotient matrices of such partitions, and characterize all these partitions for w>=4, n>2w, and for w>=7, n = 2w, up to equivalence.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-24T16:31:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B30",
      "05E99"
    ],
    "keywords": [
      "johnson graphs",
      "second eigenvalue",
      "admissible quotient matrices",
      "partitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}