{
  "id": "1806.08604",
  "version": "v1",
  "published": "2018-06-22T11:22:41.000Z",
  "updated": "2018-06-22T11:22:41.000Z",
  "title": "The Girth of Cayley graphs of Sylow 2-subgroups of symmetric groups $S_{2^n}$ on diagonal bases",
  "authors": [
    "Bartłomiej Pawlik"
  ],
  "comment": "14 pages, 1 figure",
  "categories": [
    "math.GR"
  ],
  "abstract": "A diagonal base of a Sylow 2-subgroup $P_n(2)$ of symmetric group $S_{2^n}$ is a minimal generating set of this subgroup consisting of elements with only one non-zero coordinate in the polynomial representation. For different diagonal bases Cayley graphs of $P_n(2)$ may have different girths (i.e. minimal lengths of cycles) and thus be non-isomorphic. In presented paper all possible values of girths of Cayley graphs of $P_n(2)$ on diagonal bases are calculated. A criterion for whenever such Cayley graph has girth equal to 4 is presented. A lower bound for the number of different non-isomorphic Cayley graphs of $P_n(2)$ on diagonal bases is proposed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-22T11:22:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "20B35",
      "20D20"
    ],
    "keywords": [
      "symmetric group",
      "diagonal bases cayley graphs",
      "non-isomorphic cayley graphs",
      "non-zero coordinate",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}