A polychrome labeling of a simple and connected graph \(G = (V, E)\) by an abelian group \(A\) is a bijective map from \(V\) onto \(A\) such that the induced edge labeling \(f^*(vw) = f(v) + f(w)\), \(vw \in E\), is injective. The paper completes the characterization of polychrome paths and cycles begun in [3].