Topological additive numbering of directed acyclic graphs

We characterize when a digraph has topological additive numberings, give a lower bound for ηt(D) and provide an integer programming formulation for our problem. We also present some families for which ηt(D) can be computed in polynomial time. Finally, we prove that this problem is NP-Hard even when its input is restricted to planar bipartite digraphs.