{
  "id": "math/0608198",
  "version": "v2",
  "published": "2006-08-08T18:05:39.000Z",
  "updated": "2006-10-02T22:16:38.000Z",
  "title": "Linear combinations of graph eigenvalues",
  "authors": [
    "Vladimir Nikiforov"
  ],
  "comment": "Some calculation errors from the first version have been corrected",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "Let F(G) be a fixed linear combination of the k extremal eigenvalues of a graph G and of its complement. The problem of finding max{F(G):v(G)=n} generalizes a number of problems raised previously in the literature. We show that the limit max{F(G):v(G)=n}/n exists when n tends to infinity. We also answer a question of Gernert about the sum of the two maximal eigenvalues of a graph.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-02T22:16:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50"
    ],
    "keywords": [
      "graph eigenvalues",
      "maximal eigenvalues",
      "fixed linear combination",
      "extremal eigenvalues",
      "complement"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8198N"
    }
  }
}