{
  "aliases": [
    "graceful-graph",
    "graceful-labeling-conjecture",
    "ringel-kotzig-conjecture",
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  "body": "\n## Summary\n\nIn graph theory, a **graceful labeling** of a [[graph|00C0BR7D7H]] with $m$ edges is a labeling of its vertices with some subset of the [[integers|0C4JS9RF5M]] from 0 to $m$ inclusive, such that no two vertices share a label, and each edge is uniquely identified by the [[absolute difference|0KXJTZSW9B]] between its endpoints, such that this magnitude lies between 1 and $m$ inclusive. A graph which admits a graceful labeling is called a **graceful graph**.\n",
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