On consecutive edge magic total labeling of graphs

Let G=(V,E)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 V∪EV∪E to the integers 1,2,…,n+e1,2,…,n+e, with the property that for every xy∈Exy∈E, α(x)+α(y)+α(xy)=kα(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}α(V)={a+1,…,a+n} and a b  -edge consecutive edge magic total if α(E)={b+1,b+2,…,b+e}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.