= Solution
{c}
Decode the <Prüfer code> by repeatedly attaching the smallest label absent from the remaining code to its first entry. This produces the successive edges $1\!-\!2$, $3\!-\!6$, $4\!-\!2$, $5\!-\!2$, followed by the final edge $2\!-\!6$. Thus
$$
\boxed{E=\{\{1,2\},\{3,6\},\{2,4\},\{2,5\},\{2,6\}\}.}
$$
\Image[/past-exam-of-the-probability-statistics-and-options-i-course-of-the-university-of-oxford/2008-prufer-tree.png]
{title=Decoding the Prüfer sequence gives the five displayed edges}
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