{
  "id": "1301.1794",
  "version": "v1",
  "published": "2013-01-09T09:48:48.000Z",
  "updated": "2013-01-09T09:48:48.000Z",
  "title": "A construction for infinite families of semisymmetric graphs revealing their full automorphism group",
  "authors": [
    "Philippe Cara",
    "Sara Rottey",
    "Geertrui Van de Voorde"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a general construction leading to different non-isomorphic families $\\Gamma_{n,q}(\\K)$ of connected $q$-regular semisymmetric graphs of order $2q^{n+1}$ embedded in $\\PG(n+1,q)$, for a prime power $q=p^h$, using the linear representation of a particular point set $\\K$ of size $q$ contained in a hyperplane of $\\PG(n+1,q)$. We show that, when $\\K$ is a normal rational curve with one point removed, the graphs $\\Gamma_{n,q}(\\K)$ are isomorphic to the graphs constructed for $q$ prime in [9] and to the graphs constructed for $q=p^h$ in [20]. These graphs were known to be semisymmetric but their full automorphism group was up to now unknown. For $q\\geq n+3$ or $q=p=n+2$, $n\\geq 2$, we obtain their full automorphism group from our construction by showing that, for an arc $\\K$, every automorphism of $\\Gamma_{n,q}(\\K)$ is induced by a collineation of the ambient space $\\PG(n+1,q)$. We also give some other examples of semisymmetric graphs $\\Gamma_{n,q}(\\K)$ for which not every automorphism is induced by a collineation of their ambient space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-01-09T09:48:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E20",
      "20B25"
    ],
    "keywords": [
      "full automorphism group",
      "semisymmetric graphs revealing",
      "infinite families",
      "construction",
      "ambient space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1301.1794C"
    }
  }
}