Show that each vertex $v$ of a tree $T$ appears $\deg(v)-1$ times in Prüfer sequence of $T$.
Could you do this by induction on $n$ where $n$ is the number of vertices in a graph?
So far, I have my base case $n=2$ in which case both vertices have degree $1$ and since the Prüfer encoding is empty, the base case holds.
How would I go from here? Or am I going about it in completely the wrong way?