On (super) edge-magic total labelings of a subdivision of a star S n

Abstract

Let G be a finite graph, with V(G) and E(G) the vertex-set and edgeset of G, respectively. An edge-magic total labeling is a bijection f from V(G) U E(G) to {1,2,3,... ,|V(G)| + |E(G)|} such that there exists a constant k satisfying f(u) + f(uv) + f(v) = k, for each uv € E(G). Such a labeling is called a super edge-magic total labeling if all vertices of G receive all smallest labels. In this paper, we consider (super) edge-magic total labeling for subdivision of a star S_n (with n + 1 vertices).