{
  "id": "1811.03803",
  "version": "v1",
  "published": "2018-11-09T07:36:29.000Z",
  "updated": "2018-11-09T07:36:29.000Z",
  "title": "On rationality of generating function for the number of spanning trees in circulant graphs",
  "authors": [
    "A. D. Mednykh",
    "I. A. Mednykh"
  ],
  "comment": "11 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "Let $F(x)=\\sum\\limits_{n=1}^\\infty\\tau(n)x^n$ be the generating function for the number $\\tau(n)$ of spanning trees in the circulant graphs $C_{n}(s_1,s_2,\\ldots,s_k).$ We show that $F(x)$ is a rational function with integer coefficients satisfying the property $F(x)=F(1/x).$ A similar result is also true for the circulant graphs of odd valency $C_{2n}(s_1,s_2,\\ldots,s_k,n).$ We illustrate the obtained results by a series of examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-09T07:36:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C30",
      "39A10"
    ],
    "keywords": [
      "circulant graphs",
      "spanning trees",
      "generating function",
      "rationality",
      "odd valency"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}