{
  "id": "1109.3928",
  "version": "v1",
  "published": "2011-09-19T02:35:41.000Z",
  "updated": "2011-09-19T02:35:41.000Z",
  "title": "Total and paired domination numbers of toroidal meshes",
  "authors": [
    "Fu-Tao Hu",
    "Jun-Ming Xu"
  ],
  "comment": "8 pages with 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G$ be a graph without isolated vertices. The total domination number of $G$ is the minimum number of vertices that can dominate all vertices in $G$, and the paired domination number of $G$ is the minimum number of vertices in a dominating set whose induced subgraph contains a perfect matching. This paper determines the total domination number and the paired domination number of the toroidal meshes, i.e., the Cartesian product of two cycles $C_n$ and $C_m$ for any $n\\ge 3$ and $m\\in\\{3,4\\}$, and gives some upper bounds for $n, m\\ge 5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-19T02:35:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C40",
      "05C12",
      "E.1",
      "G.2.2"
    ],
    "keywords": [
      "paired domination number",
      "toroidal meshes",
      "total domination number",
      "minimum number",
      "induced subgraph contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.3928H"
    }
  }
}