{
  "id": "1908.06859",
  "version": "v1",
  "published": "2019-08-19T14:58:38.000Z",
  "updated": "2019-08-19T14:58:38.000Z",
  "title": "Impact of Some Graph Operations on Double Roman Domination Number",
  "authors": [
    "Anu V.",
    "Aparna Lakshmanan S."
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a graph $G=(V,E)$, a function $f:V\\rightarrow \\{0,1,2,3\\}$ having the property that if $f(v)=0$, then there exist $ v_{1},v_{2}\\in N(v)$ such that $f(v_{1})=f(v_{2})=2$ or there exists $ w \\in N(v)$ such that $f(w)=3$, and if $f(v)=1$, then there exists $ w \\in N(v)$ such that $f(w)\\geq 2$ is called a double Roman dominating function (DRDF). The weight of a DRDF $f$ is the sum $f(V)=\\sum_{v\\in V}f(v)$. The double Roman domination number, $\\gamma_{dR}(G)$, is the minimum among the weights of DRDFs on $G$. In this paper, we study the impact of some graph operations, such as cartesian product, addition of twins and corona with a graph, on double Roman domination number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-19T14:58:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C76"
    ],
    "keywords": [
      "double roman domination number",
      "graph operations",
      "double roman dominating function",
      "cartesian product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}