{
  "aliases": [
    "graph-cover"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn the mathematical discipline of graph theory, a [[graph|00C0BR7D7H]] $C$ is a **covering graph** of another graph $G$ if there is a **covering map** from the vertex set of $C$ to the vertex set of $G$. A covering map $f$ is a surjection and a local isomorphism: the neighbourhood of a vertex $v$ in $C$ is mapped [[bijectively|0GG9TVW90M]] onto the neighbourhood of $f(v)$ in $G$.\n",
  "commit": "68a8c3dc73fd55004b2796431c607c30960d1a85",
  "front": {
    "aliases": [
      "graph-cover"
    ],
    "inventory": [
      "4TXK9Z6S4J"
    ],
    "kind": "concept",
    "name": "Covering graph",
    "same_as": {
      "wikidata": "Q5179252",
      "wikipedia": "Covering graph"
    },
    "sources": [
      {
        "locator": "Covering graph",
        "mention": "wikipedia://en/21123339",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:21123339@r1369278026"
      }
    ],
    "tag": "1QVTYPM0KK"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/1QVTYPM0KK/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/1QVTYPM0KK.md",
  "msc": null,
  "name": "Covering graph",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/1QV/1QVTYPM0KK.md",
  "status": null,
  "tag": "1QVTYPM0KK",
  "uri": "m2://1QVTYPM0KK",
  "url": "https://math2.tamnd.com/wiki/covering-graph/",
  "writing": {
    "tag": "1QVTYPM0KK",
    "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
      }
    ]
  }
}