{
  "id": "1103.6134",
  "version": "v1",
  "published": "2011-03-31T10:13:57.000Z",
  "updated": "2011-03-31T10:13:57.000Z",
  "title": "The Tutte polynomial and the automorphism group of a graph",
  "authors": [
    "Nafaa Chbili"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "A graph $G$ is said to be $p$-periodic, if the automorphism group $Aut(G)$ contains an element of order $p$ which preserves no edges. In this paper, we investigate the behavior of graph polynomials (Negmai and Tutte) with respect to graph periodicity. In particular, we prove that if $p$ is a prime, then the coefficients of the Tutte polynomial of such a graph satisfy a certain necessary condition. This result is illustrated by an example where the Tutte polynomial is used to rule out the periodicity of the Frucht graph.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-03-31T10:13:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C31",
      "57M15"
    ],
    "keywords": [
      "tutte polynomial",
      "automorphism group",
      "necessary condition",
      "graph satisfy",
      "graph periodicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1103.6134C"
    }
  }
}