On Zero-Sum -Magic Labelings of 3-Regular Graphs

Abstract

Let G = (V, E) be a finite loopless graph and let (A, +) be an abelian group with identity 0. Then an A-magic labeling of G is a function from E into A - {0} such that for some for every , where E(v) is the set of edges incident to v. If exists such that a = 0, then G is zero-sum A-magic. Let zim(G) denote the subset of (the positive integers) such that if and only if G is zero-sum -magic and if and only if G is zero-sum -magic. We establish that if G is 3-regular, then or.