{
  "id": "1611.09291",
  "version": "v1",
  "published": "2016-11-28T19:16:14.000Z",
  "updated": "2016-11-28T19:16:14.000Z",
  "title": "Trees with distinguishing number two",
  "authors": [
    "Saeid Alikhani",
    "Samaneh Soltani"
  ],
  "comment": "6 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has a vertex labeling with $d$ labels that is preserved only by a trivial automorphism. In this paper we characterize all trees with radius at most three and distinguishing number two. Also we present a necessary condition for trees with distinguishing number two and radius more than three.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-28T19:16:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25"
    ],
    "keywords": [
      "distinguishing number",
      "trivial automorphism",
      "necessary condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}