{
  "id": "1409.2538",
  "version": "v1",
  "published": "2014-09-08T22:09:24.000Z",
  "updated": "2014-09-08T22:09:24.000Z",
  "title": "A (forgotten) upper bound for the spectral radius of a graph",
  "authors": [
    "Clive Elphick",
    "ChiaAn Liu"
  ],
  "comment": "7 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "The best degree-based upper bound for the spectral radius is due to Liu and Weng. This paper begins by demonstrating that a (forgotten) upper bound for the spectral radius dating from 1983 is equivalent to their much more recent bound. This bound is then used to compare lower bounds for the clique number. A series of sharp upper bounds for the signless Laplacian spectral radius is then proposed as another application. Finally a new lower bound for generalised r-partite graphs is proved, by extending a result due to Erdos.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-08T22:09:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C69"
    ],
    "keywords": [
      "best degree-based upper bound",
      "signless laplacian spectral radius",
      "sharp upper bounds",
      "compare lower bounds",
      "clique number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.2538E"
    }
  }
}