{
  "id": "1407.0367",
  "version": "v1",
  "published": "2014-07-01T19:23:46.000Z",
  "updated": "2014-07-01T19:23:46.000Z",
  "title": "On the Roman Bondage Number of Graphs on surfaces",
  "authors": [
    "Vladimir Samodivkin"
  ],
  "comment": "5 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A Roman dominating function on a graph $G$ is a labeling $f : V(G) \\rightarrow \\{0, 1, 2\\}$ such that every vertex with label $0$ has a neighbor with label $2$. The Roman domination number, $\\gamma_R(G)$, of $G$ is the minimum of $\\Sigma_{v\\in V (G)} f(v)$ over such functions. The Roman bondage number $b_R(G)$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with Roman domination number not equal to $\\gamma_R(G)$. In this paper we obtain upper bounds on $b_{R}(G)$ in terms of (a) the average degree and maximum degree, and (b) Euler characteristic, girth and maximum degree. We also show that the Roman bondage number of every graph which admits a $2$-cell embedding on a surface with non negative Euler characteristic does not exceed $15$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-01T19:23:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69"
    ],
    "keywords": [
      "roman bondage number",
      "roman domination number",
      "maximum degree",
      "non negative euler characteristic",
      "smallest set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.0367S"
    }
  }
}