graph G is called edge-magic if there exists a bijective function: V (G)U E(G) →{1, 2, ... , |V (G)| + |E(G)|} such that φ(x)+φ(xy)+φ(y) is a constant c(φ) for every edge xy ∈ E(G); here c(φ) is called the valence of cp. A graph G is said to be super edge-magic if φ(V(G)) = {1, 2, ... , |V(G)|}. The super edge-magic deficiency, denoted by μ_s(G), is the minimum nonnegative integer n such that G ∪ nK_1 has a super edge-magic labeling; if such an integer does not exist we define μ_s(G) to be +∞. In this paper we study the super edge-magic deficiency of some families of graphs related to ladder graphs.
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