PrueferCode(L) returns a tree which corresponds to the Prüfer encoding of L. The input L must be a list, Vector, or 1-D Array whose elements are positive integers less than or equal to numelems(L)+2.

PrueferCode(T) returns a list of positive integers comprising the Prüfer encoding of a tree T.

$\mathrm{with}\left(\mathrm{GraphTheory}\right)\:$

$\mathrm{PrueferCode}\left(\left[6\,7\,1\,5\,2\,3\,11\,4\,9\,12\right]\right)$

$\mathrm{Graph\; 1:\; an\; undirected\; graph\; with\; 12\; vertices\; and\; 11\; edge(s)}$

$T≔\mathrm{Graph}\left(10\,\left\{\left\{1\,8\right\}\,\left\{2\,3\right\}\,\left\{2\,7\right\}\,\left\{4\,6\right\}\,\left\{5\,6\right\}\,\left\{6\,7\right\}\,\left\{6\,8\right\}\,\left\{7\,9\right\}\,\left\{8\,10\right\}\right\}\right)$

$T≔\mathrm{Graph\; 2:\; an\; undirected\; graph\; with\; 10\; vertices\; and\; 9\; edge(s)}$

$\mathrm{PrueferCode}\left(T\right)$

$\left[8\,2\,7\,6\,6\,7\,6\,8\right]$

The Prüfer encoding of a tree was first used by Heinz Prüfer to prove Cayley's formula, which states that the number of trees on n labeled vertices is $n^{n-2}$.

"Prüfer sequence", Wikipedia. https://en.wikipedia.org/wiki/Pruefer_sequence

The GraphTheory[PrueferCode] command was introduced in Maple 2021.

For more information on Maple 2021 changes, see Updates in Maple 2021.