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A graph $G$ is called edge-magic if there is a bijective function $f$ fromthe set of vertices and edges to the set $\{1,2,\ldots,|V(G)|+|E(G)|\}$ suchthat the sum $f(x)+f(xy)+f(y)$ for any $xy$ in $E(G)$ is constant. Such afunction is called an edge-magic labelling of G and the constant is called thevalence of $f$. An edge-magic labelling with the extra property that $f(V(G))=\{1,2,\ldots,|V(G)|\}$ is called super edge-magic. In this paper, we establisha relationship between the valences of (super) edge-magic labelings of certaintypes of bipartite graphs and the existence of a particular type ofdecompositions of such graphs.

(Di)graph decompositions and magic type labelings: a dual relation