{
  "id": "1109.1657",
  "version": "v1",
  "published": "2011-09-08T08:33:29.000Z",
  "updated": "2011-09-08T08:33:29.000Z",
  "title": "Complexity of Bondage and Reinforcement",
  "authors": [
    "Fu-Tao Hu",
    "Jun-Ming Xu"
  ],
  "comment": "16 pages with 3 figures",
  "categories": [
    "math.CO",
    "cs.CC"
  ],
  "abstract": "Let $G=(V,E)$ be a graph. A subset $D\\subseteq V$ is a dominating set if every vertex not in $D$ is adjacent to a vertex in $D$. A dominating set $D$ is called a total dominating set if every vertex in $D$ is adjacent to a vertex in $D$. The domination (resp. total domination) number of $G$ is the smallest cardinality of a dominating (resp. total dominating) set of $G$. The bondage (resp. total bondage) number of a nonempty graph $G$ is the smallest number of edges whose removal from $G$ results in a graph with larger domination (resp. total domination) number of $G$. The reinforcement number of $G$ is the smallest number of edges whose addition to $G$ results in a graph with smaller domination number. This paper shows that the decision problems for bondage, total bondage and reinforcement are all NP-hard.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-08T08:33:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "G.2.2"
    ],
    "keywords": [
      "total bondage",
      "smallest number",
      "complexity",
      "total domination",
      "smaller domination number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.1657H"
    }
  }
}