{
  "id": "1605.06918",
  "version": "v1",
  "published": "2016-05-23T07:29:00.000Z",
  "updated": "2016-05-23T07:29:00.000Z",
  "title": "On the Roman domination number of generalized Sierpinski graphs",
  "authors": [
    "Fatemeh Ramezani",
    "Erick D. Rodriguez-Bazan",
    "Juan A. Rodriguez-Velazquez"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A map $f : V \\rightarrow \\{0, 1, 2\\}$ is a Roman dominating function on a graph $G=(V,E)$ if for every vertex $v\\in V$ with $f(v) = 0$, there exists a vertex $u$, adjacent to $v$, such that $f(u) = 2$. The weight of a Roman dominating function is given by $f(V) =\\sum_{u\\in V}f(u)$. The minimum weight of a Roman dominating function on $G$ is called the Roman domination number of $G$. In this article we study the Roman domination number of Generalized Sierpi\\'{n}ski graphs $S(G,t)$. More precisely, we obtain a general upper bound on the Roman domination number of $S(G,t)$ and we discuss the tightness of this bound. In particular, we focus on the cases in which the base graph $G$ is a path, a cycle, a complete graph or a graph having exactly one universal vertex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-23T07:29:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C76"
    ],
    "keywords": [
      "roman domination number",
      "generalized sierpinski graphs",
      "roman dominating function",
      "general upper bound",
      "universal vertex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}