{
  "id": "1907.10137",
  "version": "v1",
  "published": "2019-07-23T21:23:40.000Z",
  "updated": "2019-07-23T21:23:40.000Z",
  "title": "Double domination and total $2$-domination in digraphs and their dual problems",
  "authors": [
    "Doost Ali Mojdeh",
    "Babak Samadi"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A subset $S$ of vertices of a digraph $D$ is a double dominating set (total $2$-dominating set) if every vertex not in $S$ is adjacent from at least two vertices in $S$, and every vertex in $S$ is adjacent from at least one vertex in $S$ (the subdigraph induced by $S$ has no isolated vertices). The double domination number (total $2$-domination number) of a digraph $D$ is the minimum cardinality of a double dominating set (total $2$-dominating set) in $D$. In this work, we investigate these concepts which can be considered as two extensions of double domination in graphs to digraphs, along with the concepts $2$-limited packing and total $2$-limited packing which have close relationships with the above-mentioned concepts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-23T21:23:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dual problems",
      "double dominating set",
      "double domination number",
      "minimum cardinality",
      "close relationships"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}