Vertex magic total labeling of middle and total graph of cycle

Abstract

A vertex magic total labeling is a bijection from the union of the vertex set and edge set to the consecutive integers 1,2,3,....,v+e with the property that for every u in the vertex set, the sum of the label of u and the label of the edges incident with u is equal to k, for some constant k. In this paper, we establish the vertex magic labeling of some classes of graphs and provide some open problems related to it.