{
  "id": "1308.1653",
  "version": "v2",
  "published": "2013-08-07T18:34:02.000Z",
  "updated": "2013-09-19T02:37:27.000Z",
  "title": "Maxima of the Q-index: graphs with bounded clique number",
  "authors": [
    "Nair Maria Maia de Abreu",
    "Vladimir Nikiforov"
  ],
  "comment": "10 pages, corrected a typo",
  "journal": "Electronic J. Linear Algebra 23 (2012), 782-789",
  "categories": [
    "math.CO"
  ],
  "abstract": "This paper gives a tight upper bound on the spectral radius of the signless Laplacian of graphs of given order and clique number. More precisely, let G be a graph of order n, let A be its adjacency matrix, and let D be the diagonal matrix of the row-sums of A. If G has clique number r, then the largest eigenvalue q(G) of the matrix Q=A+D satisfies q(G)<= 2(1-1/r)n. If G is a complete regular r-partite graph, then equality holds in the above inequality. This result confirms a conjecture of Hansen and Lucas.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-19T02:37:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "bounded clique number",
      "complete regular r-partite graph",
      "tight upper bound",
      "equality holds",
      "spectral radius"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.1653D"
    }
  }
}