Abstract
A graph G is called edge-magic if there exists a bijective function phi : V(G)boolean OR E(G) -> {1, 2,..., |V(G)|+|E(G)|} such that phi(x) + phi(xy) + phi(y) is a constant c(phi) for every edge xy is an element of E(G); here c(phi) is called the valence of phi. A graph G is said to be super edge-magic if phi(V(G)) = {1, 2,..., |V(G)|}. The super edge-magic deficiency, denoted by mu(s)(G), is the minimum nonnegative integer n such that G boolean OR nK(1) has a super edge-magic labeling; if such an integer does not exist we define mu(s)(G) to be +infinity. In this paper we study the super edge-magic deficiency of some families of graphs related to ladder graphs.