  This paper provides the generating series for the embedding of tree-like
graphs of arbitrary number of vertices, accourding to their genus. It applies
and extends the techniques of Chan, where it was used to give an alternate
proof of the Goulden and Slofstra formula. Furthermore, this greatly
generalizes the famous Harer-Zagier formula, which computes the Euler
characteristic of the moduli space of curves, and is equivalent to the
computation of one vertex maps.
