{
  "id": "1608.00769",
  "version": "v1",
  "published": "2016-08-02T11:14:13.000Z",
  "updated": "2016-08-02T11:14:13.000Z",
  "title": "On distances in generalized Sierpinski graphs",
  "authors": [
    "Alejandro Estrada-Moreno",
    "Erick D. Rodriguez-Bazan",
    "Juan A. Rodriguez-Velazquez"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we propose formulas for the distance between vertices of a generalized Sierpi\\'{n}ski graph $S(G,t)$ in terms of the distance between vertices of the base graph $G$. In particular, we deduce a recursive formula for the distance between an arbitrary vertex and an extreme vertex of $S(G,t)$, and we obtain a recursive formula for the distance between two arbitrary vertices of $S(G,t)$ when the base graph is triangle-free. From these recursive formulas, we provide algorithms to compute the distance between vertices of $S(G,t)$. In addition, we give an explicit formula for the diameter and radius of $S(G,t)$ when the base graph is a tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-02T11:14:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C76",
      "05C12"
    ],
    "keywords": [
      "generalized sierpinski graphs",
      "base graph",
      "recursive formula",
      "arbitrary vertex",
      "extreme vertex"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}