{
  "id": "2103.15288",
  "version": "v1",
  "published": "2021-03-29T02:44:53.000Z",
  "updated": "2021-03-29T02:44:53.000Z",
  "title": "Sharp bounds on the zeroth-order general Randić index of trees in terms of domination number",
  "authors": [
    "Chang Liu",
    "Jianping Li"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The zeroth-order general Randi\\'c index of graph $G=(V_G,E_G)$, denoted by $^0R_{\\alpha}(G)$, is the sum of items $(d_{v})^{\\alpha}$ over all vertices $v\\in V_G$, where $\\alpha$ is a pertinently chosen real number. In this paper, we obtain the sharp upper and lower bounds on $^0R_{\\alpha}$ of trees with a domination number $\\gamma$, in intervals $\\alpha\\in(-\\infty,0)\\cup(1,\\infty)$ and $\\alpha\\in(0,1)$, respectively. The corresponding extremal graphs of these bounds are also characterized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-29T02:44:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C35",
      "05C69"
    ],
    "keywords": [
      "domination number",
      "sharp bounds",
      "zeroth-order general randic index",
      "pertinently chosen real number",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}