{
  "id": "0812.1616",
  "version": "v1",
  "published": "2008-12-09T05:24:21.000Z",
  "updated": "2008-12-09T05:24:21.000Z",
  "title": "Program for calculating bounds on the minimum rank of a graph using Sage",
  "authors": [
    "Laura DeLoss",
    "Jason Grout",
    "Tracy McKay",
    "Jason Smith",
    "Geoff Tims"
  ],
  "comment": "30 pages, 1 Sage program",
  "categories": [
    "math.CO"
  ],
  "abstract": "The minimum rank of a simple graph $G$ is defined to be the smallest possible rank over all symmetric real matrices whose $ij$th entry (for $i\\neq j$) is nonzero whenever $\\{i,j\\}$ is an edge in $G$ and is zero otherwise. Minimum rank is a difficult parameter to compute. However, there are now a number of known reduction techniques and bounds that can be programmed on a computer; we have developed a program using the open-source mathematics software Sage to implement several techniques. In this note, we provide the source code for this program.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-09T05:24:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "15A03"
    ],
    "keywords": [
      "minimum rank",
      "calculating bounds",
      "open-source mathematics software sage",
      "symmetric real matrices",
      "th entry"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.1616D"
    }
  }
}