{
  "id": "1109.3930",
  "version": "v1",
  "published": "2011-09-19T02:54:33.000Z",
  "updated": "2011-09-19T02:54:33.000Z",
  "title": "Roman Bondage Number of a Graph",
  "authors": [
    "Fu-Tao Hu",
    "Jun-Ming Xu"
  ],
  "comment": "21 pages with 1 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "The Roman dominating function on a graph $G=(V,E)$ is a function $f: V\\rightarrow\\{0,1,2\\}$ such that each vertex $x$ with $f(x)=0$ is adjacent to at least one vertex $y$ with $f(y)=2$. The value $f(G)=\\sum\\limits_{u\\in V(G)} f(u)$ is called the weight of $f$. The Roman domination number $\\gamma_{\\rm R}(G)$ is defined as the minimum weight of all Roman dominating functions. This paper defines the Roman bondage number $b_{\\rm R}(G)$ of a nonempty graph $G=(V,E)$ to be the cardinality among all sets of edges $B\\subseteq E$ for which $\\gamma_{\\rm R}(G-B)>\\gamma_{\\rm R}(G)$. Some bounds are obtained for $b_{\\rm R}(G)$, and the exact values are determined for several classes of graphs. Moreover, the decision problem for $b_{\\rm R}(G)$ is proved to be NP-hard even for bipartite graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-19T02:54:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "E.1",
      "G.2.2"
    ],
    "keywords": [
      "roman bondage number",
      "roman dominating function",
      "roman domination number",
      "decision problem",
      "exact values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.3930H"
    }
  }
}