{
  "id": "1906.06111",
  "version": "v1",
  "published": "2019-06-14T10:15:27.000Z",
  "updated": "2019-06-14T10:15:27.000Z",
  "title": "On the Djoković-Winkler relation and its closure in subdivisions of fullerenes, triangulations, and chordal graphs",
  "authors": [
    "Sandi Klavžar",
    "Kolja Knauer",
    "Tilen Marc"
  ],
  "comment": "13 pages, 4 figures",
  "categories": [
    "math.CO",
    "cs.DM"
  ],
  "abstract": "It was recently pointed out that certain SiO$_2$ layer structures and SiO$_2$ nanotubes can be described as full subdivisions aka subdivision graphs of partial cubes. A key tool for analyzing distance-based topological indices in molecular graphs is the Djokovi\\'c-Winkler relation $\\Theta$ and its transitive closure $\\Theta^\\ast$. In this paper we study the behavior of $\\Theta$ and $\\Theta^\\ast$ with respect to full subdivisions. We apply our results to describe $\\Theta^\\ast$ in full subdivisions of fullerenes, plane triangulations, and chordal graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-14T10:15:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chordal graphs",
      "djoković-winkler relation",
      "fullerenes",
      "triangulations",
      "full subdivisions aka subdivision graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}