{
  "id": "2104.00600",
  "version": "v1",
  "published": "2021-04-01T16:32:49.000Z",
  "updated": "2021-04-01T16:32:49.000Z",
  "title": "On the average order of a dominating set of a forest",
  "authors": [
    "Aysel Erey"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We show that the average order of a dominating set of a forest graph $G$ on $n$ vertices with no isolated vertices is at most $2n/3$. Moreover, the equality is achieved if and only if every non-leaf vertex of $G$ is a support vertex with one or two leaf neighbors. Our result answers an open question of Beaton and Brown.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-01T16:32:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C31",
      "05C69"
    ],
    "keywords": [
      "average order",
      "dominating set",
      "leaf neighbors",
      "open question",
      "result answers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}