{
  "id": "2408.07707",
  "version": "v1",
  "published": "2024-08-08T02:49:50.000Z",
  "updated": "2024-08-08T02:49:50.000Z",
  "title": "Average Degree of Graphs Derived From Aperiodic Tilings",
  "authors": [
    "Xinyan Xu",
    "Darren C. Ong"
  ],
  "categories": [
    "math.CO",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider graphs derived from aperiodically ordered tilings of the plane, by treating each corner of each tile as a vertex and each side of each tile as an edge. We calculate the average degree of these graphs. For the Ammann A2 tiling, we present a closed-form formula for the average degree. For the Kite and Dart Penrose tiling, the Rhomb Penrose Tiling, and the Ammann-Beenker tiling we present numerical calculations for the average degree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-08T02:49:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "average degree",
      "aperiodic tilings",
      "closed-form formula",
      "rhomb penrose",
      "calculations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}