{
  "id": "1911.11406",
  "version": "v1",
  "published": "2019-11-26T08:49:55.000Z",
  "updated": "2019-11-26T08:49:55.000Z",
  "title": "On Gorenstein Graphs with Independence Number at Most Three",
  "authors": [
    "Mohammad Reza Oboudi",
    "Ashkan Nikseresht"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Suppose that $G$ is a simple graph on $n$ vertices and $\\alpha=\\alpha(G)$ is the independence number of $G$. Let $I(G)$ be the edge ideal of $G$ in $S=K[x_1, \\ldots, x_n]$. We say that $G$ is Gorenstein when $S/I(G)$ is so. Here, first we present a condition on $G$ equivalent to $G$ being Gorenstein and use this to get a full characterization of Gorenstein graphs with $\\alpha=2$. Then we focus on Gorenstein graphs with $\\alpha=3$ and find the number of edges and the independence polynomial of such graphs. Finally, we present a full characterization of triangle-free Gorenstein graphs with $\\alpha=3$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-26T08:49:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "13F55",
      "05E40",
      "13H10"
    ],
    "keywords": [
      "independence number",
      "full characterization",
      "triangle-free gorenstein graphs",
      "simple graph",
      "edge ideal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}