  Let $T$ be a tree on $n$ vertices. We can regard the edges of $T$ as
transpositions of the vertex set; their product (in any order) is a cyclic
permutation. All possible cyclic permutations arise (each exactly once) if and
only if the tree is a star. In this paper we find the number of realised
cycles, and obtain some results on the number of realisations of each cycle,
for other trees. We also solve the inverse problem of the number of trees which
give rise to a given cycle. On the way, we meet some familiar number sequences
including the Euler and Fuss--Catalan numbers.
