= Solution
{c}
\b[False.] In a <Prüfer code>, the degree of a label is one plus its number of occurrences. Here labels $1,\ldots,n-2$ occur once and labels $n-1,n$ do not occur. Thus the former have degree two and the latter degree one. The decoded <tree (graph theory)> is the path
$$
(n-1),1,2,\ldots,n-2,n
$$
with the evident single-edge interpretation when $n=2$. Independently, no vertex of a simple <tree (graph theory)> on $n$ vertices can have degree $n$ at all. The degree claim in the statement is therefore impossible.
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