On the super edge-magic deficiency of forests

Abstract

Let G = (V, E) be a finite, simple and undirected graph having |V(C7)| = p and \E(G)\ = q. A super edge-magic labeling of a graph G is a bijection f : V(G) U 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 € E(G). The super edge-magic deficiency of a graph G, denoted by p,(G), is the minimum nonnegative integer n such that GUnK₁ has a super edgemagic total labeling or +∞ 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.