= Solution
There are ten labels. The successive deleted <leaves of a graph> are $3,4,5,1,6,7,2,9$, paired with the respective entries $1,1,1,2,2,2,8,8$. The final two labels are $8,10$. Thus the <tree> has <edge> set
$$
\boxed{\{13,14,15,12,26,27,28,89,8\!\!\mathbin{-}\!10\}.}
$$
Here $ij$ denotes the unordered <edge> $\{i,j\}$; the last <edge> is written with a separator to distinguish label ten. Equivalently its adjacency lists are $1:\{2,3,4,5\}$, $2:\{1,6,7,8\}$, $8:\{2,9,10\}$, with all other <vertices> <leaves of a graph>. These lists make the constructed <tree> unambiguous.
Back to article page
