Abstract
A graph G is called edge -magic if there exists a bijective function phi : V (G) U E(G) -> {1,2,..., vertical bar V(G)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 phi. Moreover, G is said to be super edge -magic if phi(V (G)) = {1,2,...,vertical bar V(G)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 U nK(1), has a super edge -magic labeling, 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 Toeplitz graphs.