CentralNotice Prüfer sequence From Wikipedia, the free encyclopedia Jump to: navigation , search In combinatorial mathematics , the Prüfer sequence (also Prüfer code or Prüfer 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. Prüfer sequences were first used by Heinz Prüfer to prove Cayley's formula in 1918. [ 1 ] 1 Algorithm to convert a tree into a Prüfer sequence 1.1 Example 2 Algorithm to convert a Prüfer sequence into a tree 3 Cayley's formula 4 Other applications 5 References 6 External links Algorithm to convert a tree into a Prüfer sequence [ edit ] One can generate a labeled tree's Prüfer sequence by iteratively removing vertices from the tree until only two vertices remain. Specifically, consider a labeled tr...