{
  "id": "2005.03335",
  "version": "v1",
  "published": "2020-05-07T09:06:27.000Z",
  "updated": "2020-05-07T09:06:27.000Z",
  "title": "Maximum dissociation sets in subcubic trees",
  "authors": [
    "Lei Zhang",
    "Jianhua Tu",
    "Chunlin Xin"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "A subset of vertices in a graph $G$ is called a maximum dissociation set if it induces a subgraph with vertex degree at most 1 and the subset has maximum cardinality. The dissociation number of $G$, denoted by $\\psi(G)$, is the cardinality of a maximum dissociation set. A subcubic tree is a tree of maximum degree at most 3. In this paper, we give the lower and upper bounds on the dissociation number in a subcubic tree of order $n$ and show that the number of maximum dissociation sets of a subcubic tree of order $n$ and dissociation number $\\psi$ is at most $1.466^{4n-5\\psi+2}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-07T09:06:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C35"
    ],
    "keywords": [
      "maximum dissociation set",
      "subcubic tree",
      "dissociation number",
      "vertex degree",
      "maximum cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}