{
  "id": "1702.02568",
  "version": "v1",
  "published": "2017-02-08T15:34:12.000Z",
  "updated": "2017-02-08T15:34:12.000Z",
  "title": "The automorphism groups of Johnson graphs revisited",
  "authors": [
    "Morteza Mirafzal"
  ],
  "comment": "Research paper, submitted",
  "categories": [
    "math.CO",
    "math.GR"
  ],
  "abstract": "The Johnson graph $J(n, i)$ is defined to the graph whose vertex set is the set of all $i$-element subsets of $\\{1, . . . , n \\}$, and two vertices are adjacent whenever the cardinality of their intersection is equal to $i$-1. In Ramras and Donovan [SIAM J. Discrete Math, 25(1): 267-270, 2011], it is proved that, if $ n \\neq 2i$ then the automorphism group of $J(n, i)$ is isomorphic with the group $Sym(n)$ and it is conjectured that if $n = 2i$, then the automorphism group of $J(n, i)$ is isomorphic with the group $ Sym(n) \\rtimes Sym(2)$. In this paper we will find these results by different methods. We will prove the conjecture in the affirmative.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-08T15:34:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C69",
      "94C15"
    ],
    "keywords": [
      "automorphism group",
      "johnson graph",
      "isomorphic",
      "discrete math",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}