{
  "id": "1205.5537",
  "version": "v1",
  "published": "2012-05-24T19:25:40.000Z",
  "updated": "2012-05-24T19:25:40.000Z",
  "title": "On domination of Cartesian product of directed cycles",
  "authors": [
    "Michel Mollard"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\gamma(C_m\\Box C_n)$ be the domination number of the Cartesian product of directed cycles $C_m$ and $C_n$ for $m,n\\geq2$. Shaheen [] and Liu and al.[ ], [ ] determined the value of $\\gamma(C_m\\Box C_n)$ when $m \\leq 6$ and when both $m$ and $n$ $\\equiv 0$ $(mod\\: 3)$. In this article we give, in general, the value of $\\gamma(C_m\\Box C_n)$ when $m\\equiv 2$ $(mod\\: 3)$ and improve the known lower bound for most of the remaining cases. We also disprove the conjectured formula for the case $m$ $\\equiv 0$ $(mod\\: 3)$ appearing in \\cite{}",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-05-24T19:25:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cartesian product",
      "directed cycles",
      "domination number",
      "lower bound",
      "remaining cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.5537M"
    }
  }
}