{
  "id": "1605.05692",
  "version": "v1",
  "published": "2016-05-18T18:43:32.000Z",
  "updated": "2016-05-18T18:43:32.000Z",
  "title": "Expected values of parameters associated with the minimum rank of a graph",
  "authors": [
    "Tracy Hall",
    "Leslie Hogben",
    "Ryan Martin",
    "Bryan Shader"
  ],
  "comment": "17 pages, 2 figures",
  "journal": "Linear Algebra Appl. 433(1) (2010), 101--117",
  "doi": "10.1016/j.laa.2010.01.036",
  "categories": [
    "math.CO"
  ],
  "abstract": "We investigate the expected value of various graph parameters associated with the minimum rank of a graph, including minimum rank/maximum nullity and related Colin de Verdi\\`ere-type parameters. Let $G(v,p)$ denote the usual Erd\\H{o}s-R\\'enyi random graph on $v$ vertices with edge probability $p$. We obtain bounds for the expected value of the random variables $\\mr(G(v,p))$, $\\M(G(v,p))$, $\\nu(G(v,p))$ and $\\xi(G(v,p))$, which yield bounds on the average values of these parameters over all labeled graphs of order $v$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-18T18:43:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C80",
      "15A03"
    ],
    "keywords": [
      "expected value",
      "minimum rank/maximum nullity",
      "average values",
      "graph parameters",
      "random graph"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}