{
  "id": "1903.12333",
  "version": "v1",
  "published": "2019-03-29T02:41:01.000Z",
  "updated": "2019-03-29T02:41:01.000Z",
  "title": "Equitable 2-partitions of the Hamming graphs with the second eigenvalue",
  "authors": [
    "Ivan Mogilnykh",
    "Alexandr Valyuzhenich"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The eigenvalues of the Hamming graph $H(n,q)$ are known to be $\\lambda_i(n,q)=(q-1)n-qi$, $0\\leq i \\leq n$. The characterization of equitable 2-partitions of the Hamming graphs $H(n,q)$ with eigenvalue $\\lambda_{1}(n,q)$ was obtained by Meyerowitz in [15]. We study the equitable 2-partitions of $H(n,q)$ with eigenvalue $\\lambda_{2}(n,q)$. We show that these partitions are reduced to equitable 2-partitions of $H(3,q)$ with eigenvalue $\\lambda_{2}(3,q)$ with exception of two constructions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-29T02:41:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05B30"
    ],
    "keywords": [
      "hamming graph",
      "second eigenvalue",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}