{
  "id": "1109.3933",
  "version": "v1",
  "published": "2011-09-19T03:05:09.000Z",
  "updated": "2011-09-19T03:05:09.000Z",
  "title": "Roman Bondage Numbers of Some Graphs",
  "authors": [
    "Fu-Tao Hu",
    "Ju-Ming Xu"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A Roman dominating function on a graph $G=(V,E)$ is a function $f: V\\to \\{0,1,2\\}$ 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 dominating function is the value $f(G)=\\sum_{u\\in V} f(u)$. The Roman domination number of $G$ is the minimum weight of a Roman dominating function on $G$. The Roman bondage number of a nonempty graph $G$ is the minimum number of edges whose removal results in a graph with the Roman domination number larger than that of $G$. This paper determines the exact value of the Roman bondage numbers of two classes of graphs, complete $t$-partite graphs and $(n-3)$-regular graphs with order $n$ for any $n\\ge 5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-19T03:05:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "E.1",
      "G.2.2"
    ],
    "keywords": [
      "roman bondage number",
      "roman dominating function",
      "roman domination number larger",
      "minimum weight",
      "nonempty graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.3933H"
    }
  }
}