{
  "id": "1412.5055",
  "version": "v1",
  "published": "2014-12-09T14:39:25.000Z",
  "updated": "2014-12-09T14:39:25.000Z",
  "title": "On the automorphism group of a Johnson graph",
  "authors": [
    "Ashwin Ganesan"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The Johnson graph $J(n,i)$ is defined to the graph whose vertex set is the set of all $i$-element subsets of $\\{1,\\ldots,n\\}$, and two vertices are joined whenever the cardinality of their intersection is equal to $i-1$. In Ramras and Donovan [\\emph{SIAM J. Discrete Math}, 25(1): 267-270, 2011], it is conjectured that if $n=2i$, then the automorphism group of the Johnson graph $J(n,i)$ is $S_n \\times \\langle T \\rangle$, where $T$ is the complementation map $A \\mapsto \\{1,\\ldots,n\\} \\setminus A$. We resolve this conjecture in the affirmative. The proof uses only elementary group theory and is based on an analysis of the clique structure of the graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-09T14:39:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "johnson graph",
      "automorphism group",
      "elementary group theory",
      "element subsets",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.5055G"
    }
  }
}