  We study the boundary L_t of the Milnor fiber for the non-isolated
singularities in C^3 with equation z^m - g(x,y) = 0 where g(x,y) is a
non-reduced plane curve germ. We give a complete proof that L_t is a Waldhausen
graph manifold and we provide the tools to construct its plumbing graph. As an
example, we give the plumbing graph associated to the germs z^2 - (x^2 -
y^3)y^l = 0 with l an interger >1. We prove that the boundary of the Milnor
fiber is a Waldhausen manifold new in complex geometry, as it cannot be the
boundary of a normal surface singularity.
