On super edge-magic deficiency of volvox and dumbbell graphs

Let G=(V,E) be a finite, simple and undirected graph of order p and size q. A super edge-magic total labeling of a graph G is a bijection λ:V(G)∪E(G)→{1,2,…,p+q}, where the vertices are labeled with the numbers 1,2,…,p and there exists a constant t such that f(x)+f(xy)+f(y)=t, for every edge xy∈E(G). The super edge-magic deficiency of a graph G, denoted by μ_s(G), is the minimum nonnegative integer n such that G∪nK₁ has a super edge-magic total labeling, or it is ∞ if there exists no such n. In this paper, we are dealing with the super edge-magic deficiency of volvox and dumbbell type graphs.