{
  "id": "2404.07819",
  "version": "v1",
  "published": "2024-04-11T15:00:10.000Z",
  "updated": "2024-04-11T15:00:10.000Z",
  "title": "Generation of $3$-connected, planar line graphs",
  "authors": [
    "Phoebe Hollowbread-Smith",
    "Riccardo W. Maffucci"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We classify and construct all line graphs that are $3$-polytopes (planar and $3$-connected). Apart from a few special cases, they are all obtained starting from the medial graphs of cubic (i.e., $3$-regular) $3$-polytopes, by applying two types of graph transformations. This is similar to the generation of other subclasses of $3$-polytopes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-11T15:00:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C75",
      "05C76",
      "05C10",
      "05C40",
      "52B05",
      "52B10"
    ],
    "keywords": [
      "planar line graphs",
      "generation",
      "medial graphs",
      "special cases",
      "graph transformations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}