{
  "id": "math/9907050",
  "version": "v1",
  "published": "1999-07-08T16:04:26.000Z",
  "updated": "1999-07-08T16:04:26.000Z",
  "title": "On some extremal problems in graph theory",
  "authors": [
    "Dmitry Jakobson",
    "Igor Rivin"
  ],
  "comment": "June 1998 Preprint",
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP",
    "math.RA",
    "math.SP"
  ],
  "abstract": "In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs -- weighing the graph changes a combinatorial problem to one in analysis. We study both weighted and unweighted graphs which are extremal for these invariants. In the unweighted case we concentrate on finding extrema among all (usually) regular graphs with the same number of vertices; we also study the relationships between such graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-07-08T16:04:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C35",
      "05C85",
      "49K35",
      "90C35"
    ],
    "keywords": [
      "graph theory",
      "extremal problems",
      "expansion constants",
      "regular graphs",
      "graph invariants"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......7050J"
    }
  }
}