{
  "id": "1005.1135",
  "version": "v1",
  "published": "2010-05-07T05:45:23.000Z",
  "updated": "2010-05-07T05:45:23.000Z",
  "title": "The asymptotic number of occurrences of a subtree in trees with bounded maximum degree and an application to the Estrada index",
  "authors": [
    "Xueliang LI",
    "Yiyang Li"
  ],
  "comment": "12 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $\\mathcal {T}^{\\Delta}_n$ denote the set of trees of order $n$, in which the degree of each vertex is bounded by some integer $\\Delta$. Suppose that every tree in $\\mathcal {T}^{\\Delta}_n$ is equally likely. For any given subtree $H$, we show that the number of occurrences of $H$ in trees of $\\mathcal {T}^{\\Delta}_n$ is with mean $(\\mu_H+o(1))n$ and variance $(\\sigma_H+o(1))n$, where $\\mu_H$, $\\sigma_H$ are some constants. As an application, we estimate the value of the Estrada index $EE$ for almost all trees in $\\mathcal {T}^{\\Delta}_n$, and give an explanation in theory to the approximate linear correlation between $EE$ and the first Zagreb index obtained by quantitative analysis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-05-07T05:45:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05",
      "05C12",
      "05C30",
      "05D40",
      "05A15",
      "05A16",
      "92E10"
    ],
    "keywords": [
      "bounded maximum degree",
      "estrada index",
      "asymptotic number",
      "application",
      "occurrences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.1135L"
    }
  }
}