{
  "id": "1501.06937",
  "version": "v1",
  "published": "2015-01-27T21:41:47.000Z",
  "updated": "2015-01-27T21:41:47.000Z",
  "title": "Graphs with $2^n+6$ vertices and cyclic automorphism group of order $2^n$",
  "authors": [
    "Peteris Daugulis"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The problem of finding upper bounds for minimal vertex number of graphs with a given automorphism group is addressed in this article for the case of cyclic $2$-groups. We show that for any natural $n\\ge 2$ there is an undirected graph having $2^n+6$ vertices and automorphism group cyclic of order $2^n$. This sets a new upper bound for minimal number of vertices of undirected graphs having automorphism group $\\mathbb{Z}/2^n\\mathbb{Z}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-27T21:41:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05E18",
      "05C35",
      "05C75"
    ],
    "keywords": [
      "cyclic automorphism group",
      "minimal vertex number",
      "undirected graph",
      "automorphism group cyclic",
      "finding upper bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150106937D"
    }
  }
}