{
  "id": "2101.10185",
  "version": "v1",
  "published": "2021-01-22T15:01:36.000Z",
  "updated": "2021-01-22T15:01:36.000Z",
  "title": "Enumeration of accurate dominating sets",
  "authors": [
    "Saeid Alikhani",
    "Maryam Safazadeh",
    "Nima Ghanbari"
  ],
  "comment": "13 pages, 6 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $D\\subseteq V$ 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 $G$. A dominating set $D$ is an accurate dominating set of $G$, if no $|D|$-element subset of $V\\setminus D$ is a dominating set of $G$. The accurate domination number, $\\gamma_a(G)$, is the cardinality of a smallest accurate dominating set $D$. In this paper, after presenting preliminaries, we count the number of accurate dominating sets of some specific graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-22T15:01:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C69",
      "05C05",
      "05C75"
    ],
    "keywords": [
      "enumeration",
      "smallest accurate dominating set",
      "accurate domination number",
      "element subset",
      "cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}