{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Summary\n\nIn graph theory, the **subdivided double** is a construction used to transform a 4-regular graph into a larger 4-regular graph. It consists of two steps: subdividing every edge into a path of two edges (with a new vertex in the middle of each path), and then replacing every vertex of the original graph with two copies, both adjacent to the same subdivision vertices. Potočnik, Verret, and Wilson use the notation $\\operatorname{SDD}(G)$ to denote the subdivided double of a graph $G$. It was named as the subdivided double earlier, by Potočnik and Wilson.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "inventory": [
      "MSZ84MC9S7"
    ],
    "kind": "concept",
    "name": "Subdivided double",
    "same_as": {
      "wikidata": "Q141304267",
      "wikipedia": "Subdivided double"
    },
    "sources": [
      {
        "locator": "Subdivided double",
        "mention": "wikipedia://en/83918691",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:83918691@r1369798712"
      }
    ],
    "tag": "MABH2V5AXR"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/MABH2V5AXR/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/MABH2V5AXR.md",
  "msc": null,
  "name": "Subdivided double",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/MAB/MABH2V5AXR.md",
  "status": null,
  "tag": "MABH2V5AXR",
  "uri": "m2://MABH2V5AXR",
  "url": "https://math2.tamnd.com/wiki/subdivided-double/",
  "writing": {
    "tag": "MABH2V5AXR",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}