{
  "id": "0906.2604",
  "version": "v2",
  "published": "2009-06-15T04:45:50.000Z",
  "updated": "2009-06-16T05:47:58.000Z",
  "title": "A proof of the conjecture on hypoenergetic graphs with maximum degree $Δ\\leq 3$",
  "authors": [
    "Xueliang Li",
    "Hongping Ma"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The energy $E(G)$ of a graph $G$ is defined as the sum of the absolute values of its eigenvalues. A graph $G$ of order $n$ is said to be hypoenergetic if $E(G)<n$. Majstorovi\\'{c} et al. conjectured that complete bipartite graph $K_{2,3}$ is the only hypoenergetic connected quadrangle-containing graph with maximum degree $\\Delta \\leq 3$. This paper is devoted to giving a confirmative proof to the conjecture.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-06-16T05:47:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A18",
      "05C50",
      "05C90",
      "92E10"
    ],
    "keywords": [
      "maximum degree",
      "hypoenergetic graphs",
      "conjecture",
      "complete bipartite graph",
      "absolute values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0906.2604L"
    }
  }
}