In this paper we present a dependency graph-based methods for computing the various semantics of normal logic programs. Our method employs conjunction nodes to unambiguously represent the dependency graph of normal logic programs. The dependency graph can be transformed suitably in a semantics preserving manner and retranslated into an equivalent normal logic program. This transformed normal logic program can be augmented with a few rules written in answer set programming (ASP), and then the CLINGO system used to compute its answer sets. Depending on how these additional rules are coded in ASP, one can compute models of the original normal logic program under the well-founded semantics, the stable model semantics, or the co-stable model semantics. In each case, justification for each atom in the model is also generated. We report on the implementation of our method as well as its performance evaluation.