Abstract
A super edge-magic labeling of a graph G = (V, E) of order p and size q is a bijection f : V boolean OR E -> {i}(i=1)(p+q) such that: (1) f(u) + f(uv) + f(v) = k for all uv is an element of E; and (2) f(V) = {i}(i=1)(p). Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv is an element of E(G), u', v' is an element of V(G) and d(G)(u, u') = d(G)(v, v') < +infinity, then f(u) + f(v) = f(u') + f(v'). In this paper we introduce the concept of strong super edge-magic labeling of a graph G with respect to a linear forest F, and we study the super edge-magicness of an odd union of nonnecessarily isomorphic acyclic graphs. Furthermore, we find exponential lower bounds for the number of super edge-magic labelings of these unions. The case when G is not acyclic will be also considered.