{
  "id": "1109.3929",
  "version": "v1",
  "published": "2011-09-19T02:45:09.000Z",
  "updated": "2011-09-19T02:45:09.000Z",
  "title": "The total bondage number of grid graphs",
  "authors": [
    "Fu-Tao Hu",
    "You Lu",
    "Jun-Ming Xu"
  ],
  "comment": "15 pages with 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The total domination number of a graph $G$ without isolated vertices is the minimum number of vertices that dominate all vertices in $G$. The total bondage number $b_t(G)$ of $G$ is the minimum number of edges whose removal enlarges the total domination number. This paper considers grid graphs. An $(n,m)$-grid graph $G_{n,m}$ is defined as the cartesian product of two paths $P_n$ and $P_m$. This paper determines the exact values of $b_t(G_{n,2})$ and $b_t(G_{n,3})$, and establishes some upper bounds of $b_t(G_{n,4})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-19T02:45:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C40",
      "05C12",
      "E.1",
      "G.2.2"
    ],
    "keywords": [
      "total bondage number",
      "grid graph",
      "total domination number",
      "minimum number",
      "removal enlarges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.3929H"
    }
  }
}