On super edge-magic decomposable graphs

Let G be any graph and let {H (i) } (iaI) be a family of graphs such that when i not equal j, a(a) (iaI) E(H (i) ) = E(G) and for all i a I. In this paper we introduce the concept of {H (i) } (iaI) -super edge-magic decomposable graphs and {H (i) } (iaI) -super edge-magic labelings. We say that G is {H (i) } (iaI) -super edge-magic decomposable if there is a bijection beta: V(G) -> {1,2,..., |V(G)|} such that for each i a I the subgraph H (i) meets the following two requirements: beta(V(H (i) )) = {1,2,..., |V(H (i) )|} and {beta(a) +beta(b): ab a E(H (i) )} is a set of consecutive integers. Such function beta is called an {H (i) } (iaI) -super edge-magic labeling of G. We characterize the set of cycles C (n) which are {H (1), H (2)}-super edge-magic decomposable when both, H (1) and H (2) are isomorphic to (n/2)K (2). New lines of research are also suggested.