{
  "id": "0905.3944",
  "version": "v2",
  "published": "2009-05-25T04:53:05.000Z",
  "updated": "2009-05-26T01:37:54.000Z",
  "title": "Hypoenergetic and strongly hypoenergetic trees",
  "authors": [
    "Xueliang Li",
    "Hongping Ma"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The energy $E(G)$ of a graph $G$ is defined as the sum of the absolute values of the eigenvalues of $G$. An $n$-vertex graph is said to be hypoenergetic if $E(G)<n$ and strongly hypoenergetic if $E(G)<n-1$. In this paper, we consider hypoenergetic and strongly hypoenergetic trees. For any given $n$ and $\\Delta$, the existence of both hypoenergetic and strongly hypoenergetic trees of order $n$ and maximum degree $\\Delta$ is completely characterized.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-05-26T01:37:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C90",
      "15A18",
      "92E10"
    ],
    "keywords": [
      "strongly hypoenergetic trees",
      "maximum degree",
      "vertex graph",
      "absolute values",
      "eigenvalues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.3944L"
    }
  }
}