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The splice quotients are an interesting class of normal surface singularitieswith rational homology sphere links, defined by W. Neumann and J. Wahl. IfGamma is a tree of rational curves that satisfies certain combinatorialconditions, 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 isolatedsingularity at the origin in C^3. For f irreducible, we completelycharacterize, in terms of n and a variant of the Puiseux pairs of f, thoseX_{f,n} for which the resolution graph satisfies the combinatorial conditionsthat are necessary for splice quotients. This result is topological; whether ornot X_{f,n} is analytically isomorphic to a splice quotient is treatedseparately.

On the topology of surface singularities {z^n=f(x,y)}, for f irreducible