{
  "id": "1707.06161",
  "version": "v1",
  "published": "2017-07-19T15:37:45.000Z",
  "updated": "2017-07-19T15:37:45.000Z",
  "title": "The distinguishing number (index) and the domination number of a graph",
  "authors": [
    "Saeid Alikhani",
    "Samaneh Soltani"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The distinguishing number (index) $D(G)$ ($D'(G)$) of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling (edge labeling) with $d$ labels that is preserved only by a trivial automorphism. A set $S$ of vertices in $G$ is a dominating set of $G$ if every vertex of $V(G)\\setminus S$ is adjacent to some vertex in $S$. The minimum cardinality of a dominating set of $G$ is the domination number of $G$ and denoted by $\\gamma (G)$. In this paper, we obtain some upper bounds for the distinguishing number and the distinguishing index of a graph based on its domination number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-19T15:37:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C69"
    ],
    "keywords": [
      "domination number",
      "distinguishing number",
      "dominating set",
      "upper bounds",
      "trivial automorphism"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}