Super Vertex Magic Circulant Graphs

Let G = (V, E) be a finite simple graph with p = vertical bar V vertical bar vertices and q = vertical bar E vertical bar edges, without any isolated vertex or any isolated edge. A vertex magic total labeling of the graph G is a bijection f from V boolean OR E to the set of consecutive integers {1, 2, ..., p + q}, such that for every vertex u is an element of V, the weight f (u) + E-uv is an element of E f(uv) is constant. Moreover if f (V) = {1,2, ..., p}, f is called a super vertex magic total labeling. A graph is (super) vertex magic if it admits a (super) vertex magic total labeling. In 2002 MacDougall et al. first introduced the concept of vertex magic total labeling and studied their properties. In this paper we study the existence of super vertex magic total labelings for a class of 5-regular circulant graphs. Applications to other classes of graphs and open problems are also included.