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