{
  "id": "1910.04931",
  "version": "v1",
  "published": "2019-10-11T01:32:01.000Z",
  "updated": "2019-10-11T01:32:01.000Z",
  "title": "On the automorphism groups of graphs with twice prime valency",
  "authors": [
    "Hong Ci Liao",
    "Jing Jian Li",
    "Zai Ping Lu"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let $\\Gamma$ be a connected graph of odd order and twice prime valency, and let $G$ be a subgroup of the automorphism group of $\\Ga$. In the case where $G$ acts transitively on the edges and quasiprimitively on the vertices of $\\Ga$, we prove that either $G$ is almost simple or $G$ is a primitive group of affine type. If further $G$ is an almost simple primitive group then, with two exceptions, the socle of $G$ acts transitively on the edges of $\\Gamma$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-11T01:32:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "20B25"
    ],
    "keywords": [
      "twice prime valency",
      "odd order",
      "automorphism group acts",
      "edge set",
      "affine type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}