{
  "id": "1012.4117",
  "version": "v2",
  "published": "2010-12-18T20:18:41.000Z",
  "updated": "2011-10-25T22:51:33.000Z",
  "title": "Upper bounds for the bondage number of graphs on topological surfaces",
  "authors": [
    "Andrei Gagarin",
    "Vadim Zverovich"
  ],
  "comment": "10 pages; Updated version (April 2011); Presented at the 7th ECCC, Wolfville (Nova Scotia, Canada), May 4-6, 2011, and the 23rd BCC, Exeter (England, UK), July 3-8, 2011",
  "journal": "Discrete Math. 313 (2013), no. 11, pp. 1132-1137",
  "doi": "10.1016/j.disc.2011.10.018",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "The bondage number b(G) of a graph G is the smallest number of edges of G whose removal from G results in a graph having the domination number larger than that of G. We show that, for a graph G having the maximum vertex degree $\\Delta(G)$ and embeddable on an orientable surface of genus h and a non-orientable surface of genus k, $b(G)\\le \\min\\{\\Delta(G)+h+2, \\Delta(G)+k+1\\}$. This generalizes known upper bounds for planar and toroidal graphs.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-25T22:51:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C10",
      "57M15",
      "90B10",
      "90B25"
    ],
    "keywords": [
      "bondage number",
      "upper bounds",
      "topological surfaces",
      "maximum vertex degree",
      "domination number larger"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.4117G"
    }
  }
}