{
  "id": "1701.01416",
  "version": "v1",
  "published": "2017-01-05T18:33:32.000Z",
  "updated": "2017-01-05T18:33:32.000Z",
  "title": "Roman $\\{2\\}$-domination in graphs and graph products",
  "authors": [
    "Faezeh Alizade",
    "Hamid Reza Maimani",
    "Leila Parsaei Majd",
    "Mina Rajabi Parsa"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a graph $G=(V,E)$ of order $n$, a Roman $\\{2\\}$-dominating function $f:V\\rightarrow\\{0,1,2\\}$ has the property that for every vertex $v\\in V$ with $f(v)=0$, either $v$ is adjacent to a vertex assigned $2$ under $f$, or $v$ is adjacent to least two vertices assigned $1$ under $f$. In this paper, we classify all graphs with Roman $\\{2\\}$-domination number belonging to the set $\\{2,3,4,n-2,n-1,n\\}$. Furthermore, we obtain some results about Roman $\\{2\\}$-domination number of some graph operations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-05T18:33:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C76"
    ],
    "keywords": [
      "graph products",
      "graph operations",
      "domination number belonging",
      "dominating function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}