{
  "id": "1306.3747",
  "version": "v2",
  "published": "2013-06-17T06:39:51.000Z",
  "updated": "2014-05-08T07:47:15.000Z",
  "title": "Cayley graphs on abelian groups",
  "authors": [
    "Edward Dobson",
    "Pablo Spiga",
    "Gabriel Verret"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $A$ be an abelian group and let $\\iota$ be the automorphism of $A$ defined by $i:a\\mapsto a^{-1}$. A Cayley graph $\\Gamma=\\mathrm{Cay}(A,S)$ is said to have an automorphism group \\emph{as small as possible} if $\\mathrm{Aut}(\\Gamma)= A\\rtimes\\langle i\\rangle$. In this paper, we show that almost all Cayley graphs on abelian groups have automorphism group as small as possible, proving a conjecture of Babai and Godsil.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-05-08T07:47:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian group",
      "cayley graph",
      "automorphism group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.3747D"
    }
  }
}