{
  "id": "0804.2776",
  "version": "v1",
  "published": "2008-04-17T11:47:47.000Z",
  "updated": "2008-04-17T11:47:47.000Z",
  "title": "Largest Laplacian Eigenvalue and Degree Sequences of Trees",
  "authors": [
    "Tuerker Biyikoglu",
    "Marc Hellmuth",
    "Josef Leydold"
  ],
  "comment": "9 pages, 2 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate the structure of trees that have greatest maximum eigenvalue among all trees with a given degree sequence. We show that in such an extremal tree the degree sequence is non-increasing with respect to an ordering of the vertices that is obtained by breadth-first search. This structure is uniquely determined up to isomorphism. We also show that the maximum eigenvalue in such classes of trees is strictly monotone with respect to majorization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-17T11:47:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C75",
      "05C05",
      "05C50"
    ],
    "keywords": [
      "largest laplacian eigenvalue",
      "degree sequence",
      "greatest maximum eigenvalue",
      "extremal tree",
      "breadth-first search"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.2776B"
    }
  }
}