On super edge-magic graphs which are weak magic

A (p,q) graph G is total edge-magic if there exits a bijection f: Vu E ~ {1.2,. .. ,p+q} such that for each e=(u,v) in E, we have feu) + fee) + f(v) as a constant. For a graph G, denote M(G) the set of all total edge-magic labelings. The magic strength of G is the minimum of all constants among all labelings in M(G), and denoted by emt(G). The maximum of all constants among M(G) is called the maximum magic strength of G and denoted by eMt(G). Hegde and Shetty classify a magic graph as strong if emt(G) = eMt(G), ideal magic if I S eMt(G)-emt(G) S p and weak magic, if eMt(G)-emt(G) > p. A total edge­ magic graph is called a super edge-magic if f(V(G»= {I ,2, ... ,p} .The problem of identifying which kinds of super edge-magic graphs are weak-magic graphs is addressed in this paper.