Super edge-magic deficiency of graphs
Abstract
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.
