Let H be a hypergraph with a vertex set V and a hyperedge set E. Generalized from the super edge-magic in a graph, we say that a hypergraph H is super edge-magic if there is a bijection f : V ∪ E → {1,2,3, … , |V| + |E|} which satisfies: (i) there exists a constant Λ such that for all e ∈ E, f(e) + ∑v∈ef(v) = Λ and (ii) f(V) = {1,2,3, … , |V|} . In this paper, we give a necessary condition for a k-uniform hypergraph to be super edge-magic. We show that the complete k-uniform hypergraph of n vertices is super edge-magic if and only if k∈ {0,1, n - 1,n}. Finally, we also prove that the complete k-uniform k-partite hypergraph with the same number of vertices in each partite, namely n, is super edge-magic if and only if (n, k) = (1, k) for all k ≥ 2 and (n, k) = (2, 3).
