On the super edge-magic deficiencies of graphs

A graph G is called edge-magic if there exists a bijection f : V (G) ∪ E(G) → {1, 2, 3, . . . , |V (G) ∪ E(G)|} such that f(x) + f(xy) + f(y) is a constant for every edge xy ∈ E(G). A graph G is said to be super edgemagic if f(V (G)) = {1, 2, 3, . . . , |V (G)|}. Furthermore, the edge-magic deficiency of a graph G, μ(G), is defined as the minimum nonnegative integer n such thatG∪nK1 is edge-magic. Similarly, the super edge-magic deficiency of a graphG, μs(G), is either the minimum nonnegative integer n such that G ∪ nK1 is super edge-magic or +∞ if there exists no such integer n. In this paper, we present the super edge-magic deficiencies of some classes of graphs.