{
  "id": "2103.03053",
  "version": "v1",
  "published": "2021-03-04T14:22:17.000Z",
  "updated": "2021-03-04T14:22:17.000Z",
  "title": "Graphs with disjoint 2-dominating sets",
  "authors": [
    "Michael A. Henning",
    "Jerzy Topp"
  ],
  "comment": "9 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "A subset $D\\subseteq V_G$ is a dominating set of $G$ if every vertex in $V_G\\setminus D$ has a neighbor in $D$, while $D$ is a 2-dominating set of $G$ if every vertex belonging to $V_G\\setminus D$ is joined by at least two edges with a vertex or vertices in $D$. A graph $G$ is a $(2,2)$-dominated graph if it has a pair $(D,D')$ of disjoint $2$-dominating sets of vertices of $G$. In this paper we present two characterizations of minimal $(2,2)$-dominated graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-04T14:22:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C85"
    ],
    "keywords": [
      "dominating set",
      "dominated graph",
      "characterizations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}