  The splice quotients are an interesting class of normal surface singularities
with rational homology sphere links, defined by W. Neumann and J. Wahl. If
Gamma is a tree of rational curves that satisfies certain combinatorial
conditions, then there exist splice quotients with resolution graph Gamma.
Suppose the equation z^n=f(x,y) defines a surface X_{f,n} with an isolated
singularity at the origin in C^3. For f irreducible, we completely
characterize, in terms of n and a variant of the Puiseux pairs of f, those
X_{f,n} for which the resolution graph satisfies the combinatorial conditions
that are necessary for splice quotients. This result is topological; whether or
not X_{f,n} is analytically isomorphic to a splice quotient is treated
separately.
