Abstract
Let G = (V, E) be a finite, simple and undirected graph having vertical bar V(G)vertical bar = p and vertical bar E(G)vertical bar = q. A super edge-magic labeling of a graph G is a bijection f : V(G) boolean OR E(G) -> {1, 2, ... , p + q}, where f (V (G)) = {1,2,..., p} and there exists a constant c such that f(u) + f (uv) + f(v) = c, for every edge uv is an element of E(G). The super edge-magic deficiency of a graph C, denoted by mu(s)(G), is the minimum nonnegative integer n such that G boolean OR nK(1) has a super edge-magic total labeling or +infinity if there exists no such n. In this paper, we study the super edge-magic deficiencies of a forest consisting of at most three components. In particular, we determine the super edge-magic deficiency of a forest formed by paths, stars, comb, banana trees, and subdivisions of K(1,3).