{
  "id": "1308.4341",
  "version": "v1",
  "published": "2013-08-20T16:09:51.000Z",
  "updated": "2013-08-20T16:09:51.000Z",
  "title": "Maxima of the Q-index: graphs without long paths",
  "authors": [
    "Vladimir Nikiforov",
    "Xiying Yuan"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper gives tight upper bound on the largest eigenvalue q(G) of the signless Laplacian of graphs with no paths of given order. The main ingredient of our proof is a stability result of its own interest, about graphs with large minimum degree and with no long paths. This result extends previous work of Ali and Staton.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-20T16:09:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "long paths",
      "tight upper bound",
      "large minimum degree",
      "result extends",
      "main ingredient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4341N"
    }
  }
}