On the Super Edge-Magic Deficiency of Forests

Let G = (V, E) be a finite and simple graph with vertex set V(G) and edge set E(G), having order p and size q. A graph G is called super edge-magic if there exists a bijection f : V(G). E(G) -> {1, 2, ..., p + q} such that f (V(G)) = {1, 2, ..., p} and f (u) + f (uv) + f (v) = k, for every edge uv is an element of E(G). The super edge-magic deficiency of a graph G, denoted by mu(s)(G), is either the minimum nonnegative integer n such that G boolean OR nK(1) is super edge-magic or +infinity if there exists no such n. In this paper, we study the super edge-magic deficiency of forests where its components are subdivided stars or paths.