On Barycentric-Magic Graphs

Let A be an abelian group. A graph G = (V;E) is said to be A-barycentric-magic if there exists a labeling l : E(G) ??! A n f0g such that the induced vertex set labeling l+ : V (G) ??! A dened by l+(v) = P uv2E(G) l(uv) is a constant map and also satises that l+(v) = deg(v)l(uvv) for all v 2 V , and for some vertex uv adjacent to v. In this paper we determine all h 2 N for which a given graph G is Zh-barycentricmagic and characterize Zh-barycentric-magic labeling for some graphs containing vertices of degree 2 and 3.