{
  "id": "1710.03308",
  "version": "v1",
  "published": "2017-10-09T20:48:24.000Z",
  "updated": "2017-10-09T20:48:24.000Z",
  "title": "On accurate domination in graphs",
  "authors": [
    "Joanna Cyman",
    "Michael A. Henning",
    "Jerzy Topp"
  ],
  "comment": "12 pages, 1 figure",
  "categories": [
    "math.CO"
  ],
  "abstract": "A dominating set of a graph $G$ is a subset $D \\subseteq V_G$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of a smallest dominating set of $G$, denoted by $\\gamma(G)$, is the domination number of $G$. The accurate domination number of $G$, denoted by $\\gamma_{\\rm a}(G)$, is the cardinality of a smallest set $D$ that is a dominating set of $G$ and no $|D|$-element subset of $V_G \\setminus D$ is a dominating set of $G$. We study graphs for which the accurate domination number is equal to the domination number. In particular, all trees $G$ for which $\\gamma_{\\rm a}(G) = \\gamma(G)$ are characterized. Furthermore, we compare the accurate domination number with the domination number of different coronas of a graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-09T20:48:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C05",
      "05C75",
      "05C76"
    ],
    "keywords": [
      "accurate domination number",
      "study graphs",
      "cardinality",
      "smallest dominating set",
      "smallest set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}