  A dessin d'enfant, or dessin, is a bicolored graph embedded into a Riemann
surface. Acyclic dessins can be described analytically by pre-images of certain
polynomials, called Shabat polynomials, and also algebraically by their
monodromy groups, that is, the group generated by rotations of edges about
black and white vertices. In this paper we investigate the Shabat polynomials
and monodromy groups of planar acyclic dessins that are uniquely determined by
their passports.
