{
  "id": "1505.05771",
  "version": "v1",
  "published": "2015-05-21T15:40:08.000Z",
  "updated": "2015-05-21T15:40:08.000Z",
  "title": "Cayley graphs of more than one abelian group",
  "authors": [
    "Edward Dobson",
    "Joy Morris"
  ],
  "comment": "20 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "We show that for certain integers $n$, the problem of whether or not a Cayley digraph $\\Gamma$ of $\\mathbb Z_n$ is also isomorphic to a Cayley digraph of some other abelian group $G$ of order $n$ reduces to the question of whether or not a natural subgroup of the full automorphism group contains more than one regular abelian group up to isomorphism (as opposed to the full automorphism group). A necessary and sufficient condition is then given for such circulants to be isomorphic to Cayley digraphs of more than one abelian group, and an easy-to-check necessary condition is provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-21T15:40:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cayley graphs",
      "cayley digraph",
      "full automorphism group contains",
      "easy-to-check necessary condition",
      "regular abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150505771D"
    }
  }
}