{
  "id": "1702.02095",
  "version": "v1",
  "published": "2017-02-07T16:52:10.000Z",
  "updated": "2017-02-07T16:52:10.000Z",
  "title": "More odd graph theory from another point of view",
  "authors": [
    "S. Morteza Mirafzal"
  ],
  "comment": "research paper",
  "categories": [
    "math.GR"
  ],
  "abstract": "Let $ k$ be a positive integer with $ k \\geq 2 $, and $ n= 2k+1$. We denote by $ O_k $ the graph with the $ k $ element subsets of $ I = \\{ 1,2,...,n \\} $ as vertices, where two such vertices are adjacent if they are disjoint. we roll call a graph $ \\Gamma $ a $ VTNC$-graph, if it is a vertex transitive non-Cayley graph. In [7 ] it has been proved that $ O_k $ is a $ VTNC$-graph. The methods which used by the author to obtain the result, need some deep results from permutation group theory. In this paper we will show that $ O_k $ is a $ VTNC$-graph, by using rather elementary facts of number theory and group theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-07T16:52:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C69",
      "94C15"
    ],
    "keywords": [
      "odd graph theory",
      "permutation group theory",
      "vertex transitive non-cayley graph",
      "element subsets",
      "deep results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}