{
  "id": "2406.04753",
  "version": "v1",
  "published": "2024-06-07T08:53:04.000Z",
  "updated": "2024-06-07T08:53:04.000Z",
  "title": "Differential equations satisfied by generating functions of 5-, 6-, and 7-regular labelled graphs: a reduction-based approach",
  "authors": [
    "Frédéric Chyzak",
    "Marni Mishna"
  ],
  "categories": [
    "math.CO",
    "cs.SC"
  ],
  "abstract": "By a classic result of Gessel, the exponential generating functions for $k$-regular graphs are D-finite. Using Gr\\\"obner bases in Weyl algebras, we compute the linear differential equations satisfied by the generating function for 5-, 6-, and 7- regular graphs. The method is sufficiently robust to consider variants such as graphs with multiple edges, loops, and graphs whose degrees are limited to fixed sets of values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-07T08:53:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "12H05"
    ],
    "keywords": [
      "labelled graphs",
      "reduction-based approach",
      "regular graphs",
      "linear differential equations",
      "classic result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}