On consecutive edge magic total labeling of graphs

Let G=(V,E) be a finite (non-empty) graph, where V and E are the sets of vertices and edges of G. An edge magic total labeling is a bijection α from VE to the integers 1,2,…,n+e, with the property that for every xyE, α(x)+α(y)+α(xy)=k, for some constant k. Such a labeling is called an a-vertex consecutive edge magic total labeling if α(V)={a+1,…,a+n} and a b-edge consecutive edge magic total if α(E)={b+1,b+2,…,b+e}. In this paper we study the properties of a-vertex consecutive edge magic and b-edge consecutive edge magic graphs.