{
  "id": "1812.07199",
  "version": "v1",
  "published": "2018-12-18T06:59:11.000Z",
  "updated": "2018-12-18T06:59:11.000Z",
  "title": "The Hessians of the complete and complete bipartite graphs and its application to the strong Lefschetz property",
  "authors": [
    "Akiko Yazawa"
  ],
  "comment": "19 pages",
  "categories": [
    "math.CO",
    "math.AC"
  ],
  "abstract": "We consider the Hessian matrix of the weighted generating function for spanning trees. We call it the Hessian matrix of a graph. In this paper, we show that the Hessians of the complete and the complete bipartite graphs do not vanish by calculating the eigenvalues of the Hessian matrix of the graphs. As an application, we show the strong Lefschetz property for the Artinian Gorenstein algebra associated to the graphic matroids of the complete and complete bipartite graphs with at most five vertices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-18T06:59:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete bipartite graphs",
      "strong lefschetz property",
      "hessian matrix",
      "application",
      "artinian gorenstein algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}