= Solution
Take a root $r$ with children $a,b$. Give $a$ the children $c,1$, give $c$ the children $2,3$, and give $b$ the children $4,5$. The <root of a tree> has degree two, the three <vertices> $a,b,c$ have degree three, and $1,\ldots,5$ are the five <leaves of a graph>. There are nine <vertices> and eight <edges>, as required by the <handshaking lemma> and the <edge> count for a <tree>.
\Image[/past-exam-of-the-probability-statistics-and-options-ii-course-of-the-university-of-oxford/2007-tree-and-dual.png]
{title=A plane <tree> and its one-vertex <dual graph>, with two alternating face colours}
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