{
  "id": "1411.4922",
  "version": "v1",
  "published": "2014-11-18T17:30:59.000Z",
  "updated": "2014-11-18T17:30:59.000Z",
  "title": "On some automorphism related parameters in graphs",
  "authors": [
    "Imran Javaid",
    "Hira Benish",
    "Usman Ali",
    "M. Murtaza"
  ],
  "comment": "10 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we deduce some properties of f-sets of connected graphs. We introduce the concept of fixing share of each vertex of a fixing set D to see the participation of each vertex in fixing a connected graph G. We also define a parameter, called the fixing percentage, by using the concept of fixing share, which is helpful in determining the measure of the amount of fixing done by the elements of a fixing set D in G. It is shown that for every positive integer N, there exists a graph G with dtr(G)-Det(G)>= N, where dtr(G) is the determined number and Det(G) is the determining number of G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-18T17:30:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism related parameters",
      "fixing share",
      "fixing set",
      "connected graph",
      "properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.4922J"
    }
  }
}