The boundary of the Milnor fiber of the singularity f(x,y)+zg(x,y)=0

Let f , g ∈ C { x , y } be germs of functions defining plane curve singularities without common components in and let Φ ( x , y , z ) = f ( x , y ) + z g ( x , y ) . We give an explicit algorithm producing a plumbing graph for the boundary of the Milnor fiber of Φ in terms of a common resolution for f and g . We give an example of a choice for f and g yielding a boundary of a Milnor fiber having more than one irreducible component.