{
  "id": "1003.2028",
  "version": "v1",
  "published": "2010-03-10T06:34:23.000Z",
  "updated": "2010-03-10T06:34:23.000Z",
  "title": "Zero forcing parameters and minimum rank problems",
  "authors": [
    "Francesco Barioli",
    "Wayne Barrett",
    "Shaun M. Fallat",
    "H. Tracy Hall",
    "Leslie Hogben",
    "Bryan Shader",
    "P. van den Driessche",
    "Hein van der Holst"
  ],
  "comment": "14 pages, 2 figures. To appear in Linear Algebra and its Applications.",
  "categories": [
    "math.CO"
  ],
  "abstract": "The zero forcing number Z(G), which is the minimum number of vertices in a zero forcing set of a graph G, is used to study the maximum nullity / minimum rank of the family of symmetric matrices described by G. It is shown that for a connected graph of order at least two, no vertex is in every zero forcing set. The positive semidefinite zero forcing number Z_+(G) is introduced, and shown to be equal to |G|-OS(G), where OS(G) is the recently defined ordered set number that is a lower bound for minimum positive semidefinite rank. The positive semidefinite zero forcing number is applied to the computation of positive semidefinite minimum rank of certain graphs. An example of a graph for which the real positive symmetric semidefinite minimum rank is greater than the complex Hermitian positive semidefinite minimum rank is presented.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-03-10T06:34:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "05C85",
      "05C83",
      "15A03",
      "15A18",
      "05C40",
      "05C75",
      "68R10"
    ],
    "keywords": [
      "minimum rank problems",
      "positive semidefinite minimum rank",
      "zero forcing parameters",
      "symmetric semidefinite minimum rank",
      "positive semidefinite zero forcing number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1003.2028B"
    }
  }
}