Super edge-magic deficiency of graphs

Let G = (V, E) be a finite, simple and undirected graph with p vertices and q edges. An edge-magic total labeling of a graph G is a bijection f: V(G) ∪ E(G) → {1, 2,...,p + q}, where there exists a constant k such that f(u)+f(uυ)+f(υ) = k, for every edge uυ ∈ E(G). Moreover, if the vertices are labeled with the numbers 1, 2,..., p such a labeling is called a super edge-magic total labeling. The super edge-magic deficiency of a graph G, denoted by μ _s,(G), is the minimum nonnegative integer n such that G∪nK ₁ has a super edge-magic total labeling or ∞ if there exists no such n. In this paper we study the super edge-magic deficiencies of web graph Wb _n,m, Jahangir graph J _2,n, crown products L _n⊙K ₁, K ₄⊙ nK ₁ and we give an exact value of super edge-magic deficiency for one class of lobster tree.