How do I find the number $e(n)$ of trees with $n+1$unlabeled vertices $n$ labeled edges.
We're suppose to give a simple bijective proof, I guess?
Help appreciated!
2026-04-08 20:48:53.1775681333
Number $e(n)$ of trees with $n+1$ unlabeled vertices $n$ labeled edges
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Hint: Given an edge labeled tree $T$ with $n$ edges, choose a vertex of $T$ in $n+1$ ways and label it $0$. Then "push" each edge label to the vertex of that edge farthest from $0$.