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Given a rational homology sphere M, whose splice diagram satisfy thesemigroup condition, Neumann and Wahl were able to define a completeintersection surface singularity called splice diagram singularity from thesplice diagram of M. They were also able to show that under an additionalhypothesis on M called the congruence condition, the link of the splice diagramsingularity is the universal abelian cover of M. In this article we generalizethe congruence condition to the class of orbifolds called graph orbifold. Weshow that under a small additional hypothesis, this orbifold congruencecondition implies that the link or the splice diagram equations is theuniversal abelian cover. We also show that any two node splice diagramsatisfying the semigroup condition, is the splice diagram of a graph orbifoldsatisfying the orbifold congruence condition.

Splice diagram singularities and the universal abelian cover of graph orbifolds