{
  "id": "1610.07200",
  "version": "v1",
  "published": "2016-10-23T16:48:34.000Z",
  "updated": "2016-10-23T16:48:34.000Z",
  "title": "Distinguishing number and distinguishing index of Kronecker product of two graphs",
  "authors": [
    "Saeid Alikhani",
    "Samaneh Soltani"
  ],
  "comment": "10 pages, 3 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. The Kronecker product $G\\times H$ of two graphs $G$ and $H$ is the graph with vertex set $V (G)\\times V (H)$ and edge set $\\{\\{(u, x), (v, y)\\} | \\{u, v\\} \\in E(G) ~and ~\\{x, y\\} \\in E(H)\\}$. In this paper we study the distinguishing number and the distinguishing index of Kronecker product of two graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-23T16:48:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C15",
      "05C60"
    ],
    "keywords": [
      "kronecker product",
      "distinguishing number",
      "distinguishing index",
      "edge set",
      "vertex set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}