A simple graph G = (V,E) admits an H-covering if every edge in E is contained in a subgraph H ′ = (V , E) of G which is isomorphic to H . In this case we say that G is H-supermagic if there is a bijection f : V ∪ E → {1, . . . |V | + |E|} such that f(V ) = {1, . . . , |V |} and ∑ v∈V (H) f(v) + ∑ e∈E(H) f(e) is constant over all subgraphs H ′ of G which are isomorphic to H . In this paper, we s...