{
  "id": "math/0608329",
  "version": "v2",
  "published": "2006-08-14T18:48:08.000Z",
  "updated": "2006-10-02T22:13:35.000Z",
  "title": "Eigenvalues and forbidden subgraphs I",
  "authors": [
    "Vladimir Nikiforov"
  ],
  "comment": "Some calculation errors in the first version are corrected",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "We present sharp inequalities relating the number of vertices, edges, and triangles of a graph to the smallest eigenvalue of its adjacency matrix and the largest eigenvalue of its Laplacian.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-02T22:13:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "forbidden subgraphs",
      "smallest eigenvalue",
      "adjacency matrix",
      "largest eigenvalue",
      "sharp inequalities relating"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8329N"
    }
  }
}