{
  "id": "1309.5178",
  "version": "v2",
  "published": "2013-09-20T05:46:44.000Z",
  "updated": "2014-08-14T02:05:19.000Z",
  "title": "Edge-signed graphs with smallest eigenvalue greater than -2",
  "authors": [
    "Gary Greaves",
    "Jack Koolen",
    "Akihiro Munemasa",
    "Yoshio Sano",
    "Tetsuji Taniguchi"
  ],
  "comment": "25 pages",
  "doi": "10.1016/j.jctb.2014.07.006",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a structural classification of edge-signed graphs with smallest eigenvalue greater than -2. We prove a conjecture of Hoffman about the smallest eigenvalue of the line graph of a tree that was stated in the 1970s. Furthermore, we prove a more general result extending Hoffman's original statement to all edge-signed graphs with smallest eigenvalue greater than -2. Our results give a classification of the special graphs of fat Hoffman graphs with smallest eigenvalue greater than -3.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-08-14T02:05:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smallest eigenvalue greater",
      "edge-signed graphs",
      "result extending hoffmans original statement",
      "general result extending hoffmans original",
      "fat hoffman graphs"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.5178G"
    }
  }
}