{
  "id": "1607.08832",
  "version": "v1",
  "published": "2016-07-29T14:38:44.000Z",
  "updated": "2016-07-29T14:38:44.000Z",
  "title": "A note on the order of iterated line digraphs",
  "authors": [
    "C. Dalfó",
    "M. A. Fiol"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Given a digraph $G$, we propose a new method to find the recurrence equation for the number of vertices $n_k$ of the $k$-iterated line digraph $L^k(G)$, for $k\\geq0$, where $L^0(G)=G$. We obtain this result by using the minimal polynomial of a quotient digraph $\\pi(G)$ of $G$. We show some examples of this method applied to the so-called cyclic Kautz, the unicyclic, and the acyclic digraphs. In the first case, our method gives the enumeration of the ternary length-2 squarefree words of any length.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-29T14:38:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C20",
      "05C50"
    ],
    "keywords": [
      "iterated line digraph",
      "recurrence equation",
      "minimal polynomial",
      "quotient digraph",
      "cyclic kautz"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}