{
  "id": "2006.08892",
  "version": "v1",
  "published": "2020-06-16T03:06:08.000Z",
  "updated": "2020-06-16T03:06:08.000Z",
  "title": "The maximal tree with respect to the exponential of the second Zagreb index",
  "authors": [
    "Mingyao Zeng",
    "Hanyuan Deng"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "The second Zagreb index is $M_2(G)=\\sum_{uv\\in E(G)}d_{G}(u)d_{G}(v)$. It was found to occur in certain approximate expressions of the total $\\pi$-electron energy of alternant hydrocarbons and used by various researchers in their QSPR and QSAR studies. Recently the exponential of a vertex-degree-based topological index was introduced. It is known that among all trees with $n$ vertices, the exponential of the second Zagreb index $e^{M_2}$ attains its minimum value in the path $P_n$. In this paper, we show that $e^{M_2}$ attains its maximum value in the balanced double star with $n$ vertices and solve an open problem proposed by Cruz and Rada [R. Cruz, J. Rada, The path and the star as extremal values of vertex-degree-based topological indices among trees, MATCH Commun. Math. Comput. Chem. 82 (3) (2019) 715-732].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-16T03:06:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "second zagreb index",
      "maximal tree",
      "exponential",
      "vertex-degree-based topological index",
      "electron energy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}