{
  "id": "math/0609475",
  "version": "v1",
  "published": "2006-09-17T08:16:57.000Z",
  "updated": "2006-09-17T08:16:57.000Z",
  "title": "Enumeration of subtrees of trees",
  "authors": [
    "Weigen Yan",
    "Yeong-Nan Yeh"
  ],
  "comment": "20 pages, 11 figures",
  "doi": "10.1016/j.tcs.2006.09.002",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $T$ be a weighted tree. The weight of a subtree $T_1$ of $T$ is defined as the product of weights of vertices and edges of $T_1$. We obtain a linear-time algorithm to count the sum of weights of subtrees of $T$. As applications, we characterize the tree with the diameter at least $d$, which has the maximum number of subtrees, and we characterize the tree with the maximum degree at least $\\Delta$, which has the minimum number of subtrees.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-17T08:16:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C05"
    ],
    "keywords": [
      "enumeration",
      "minimum number",
      "maximum degree",
      "maximum number",
      "linear-time algorithm"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9475Y"
    }
  }
}