{
  "id": "1103.2419",
  "version": "v1",
  "published": "2011-03-12T03:56:44.000Z",
  "updated": "2011-03-12T03:56:44.000Z",
  "title": "Roman domination number of Generalized Petersen Graphs P(n,2)",
  "authors": [
    "Haoli Wang",
    "Xirong Xu",
    "Yuansheng Yang",
    "Chunnian Ji"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A $Roman\\ domination\\ function$ on a graph $G=(V, E)$ is a function $f:V(G)\\rightarrow\\{0,1,2\\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The $weight$ of a Roman domination function $f$ is the value $f(V(G))=\\sum_{u\\in V(G)}f(u)$. The minimum weight of a Roman dominating function on a graph $G$ is called the $Roman\\ domination\\ number$ of $G$, denoted by $\\gamma_{R}(G)$. In this paper, we study the {\\it Roman domination number} of generalized Petersen graphs P(n,2) and prove that $\\gamma_R(P(n,2)) = \\lceil {\\frac{8n}{7}}\\rceil (n \\geq 5)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-12T03:56:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "roman domination number",
      "generalized petersen graphs",
      "roman domination function",
      "minimum weight",
      "roman dominating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.2419W"
    }
  }
}