Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In combinatorial mathematics, the Prufer sequence (also Prufer code or Prufer numbers) of a labeled tree is a unique sequence associated with the tree. The sequence for a tree on n vertices has length n – 2, and can be generated by a simple iterative algorithm. Prufer sequences were first used by Heinz Prufer to prove Cayley's formula in 1918. One can generate a labeled tree's Prufer sequence by iteratively removing vertices from the tree until only two vertices remain. Specifically, consider a labeled tree T with vertices {1, 2, ..., n}. At step i, remove the leaf with the smallest label and set the ith element of the Prufer sequence to be the label of this leaf's neighbour. The Prufer sequence of a labeled tree is unique up to isomorphism and has length n – 2.

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