{
  "id": "1308.2096",
  "version": "v1",
  "published": "2013-08-09T11:47:56.000Z",
  "updated": "2013-08-09T11:47:56.000Z",
  "title": "Defensive alliances in graphs: a survey",
  "authors": [
    "Ismael González Yero",
    "Juan A. Rodríguez-Velázquez"
  ],
  "comment": "25 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "A set $S$ of vertices of a graph $G$ is a defensive $k$-alliance in $G$ if every vertex of $S$ has at least $k$ more neighbors inside of $S$ than outside. This is primarily an expository article surveying the principal known results on defensive alliances in graph. Its seven sections are: Introduction, Computational complexity and realizability, Defensive $k$-alliance number, Boundary defensive $k$-alliances, Defensive alliances in Cartesian product graphs, Partitioning a graph into defensive $k$-alliances, and Defensive $k$-alliance free sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-09T11:47:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "defensive alliances",
      "alliance free sets",
      "cartesian product graphs",
      "neighbors inside",
      "alliance number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.2096G"
    }
  }
}