{
  "id": "1309.0087",
  "version": "v2",
  "published": "2013-08-31T09:40:56.000Z",
  "updated": "2014-02-15T23:42:12.000Z",
  "title": "On the determinant of hexagonal grids $H_{k,n}$",
  "authors": [
    "Anna Bień"
  ],
  "comment": "9 pages, 4 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "We analyse the problem of singularity of graphs for hexagonal grid graphs. We introduce methods for transforming weighted graph, which do not change the determinant of adjacency matrix. We use these methods to calculate the determinant of all hexagonal grid graphs which describe certain hexagon-shaped benzenoid systems. The final result is the explicit formula for the determinant of graphs $H_{k,n}$. From the theorem we draw the conclusion, that all graphs of this kind are non-singular.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-15T23:42:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C75",
      "05C22",
      "G.2.2"
    ],
    "keywords": [
      "determinant",
      "hexagonal grid graphs",
      "adjacency matrix",
      "hexagon-shaped benzenoid systems",
      "final result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.0087B"
    }
  }
}