{
  "id": "1906.12202",
  "version": "v1",
  "published": "2019-06-28T13:20:35.000Z",
  "updated": "2019-06-28T13:20:35.000Z",
  "title": "On extremal results of multiplicative Zagreb indices of trees with given distance $k$-domination number",
  "authors": [
    "Fazal Hayat"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The first multiplicative Zagreb index $\\Pi_1$ of a graph $G$ is the product of the square of every vertex degree, while the second multiplicative Zagreb index $\\Pi_2$ is the product of the products of degrees of pairs of adjacent vertices. In this paper, we give sharp lower bound for $\\Pi_1$ and upper bound for $\\Pi_2$ of trees with given distance $k$-domination number, and characterize those trees attaining the bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-28T13:20:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "domination number",
      "extremal results",
      "first multiplicative zagreb index",
      "sharp lower bound",
      "second multiplicative zagreb index"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}