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 V ∪E to the integers 1,2, . . . , n+e, with the property that for every xy ∈E, 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. © 2006 Elsevier B.V. All rights reserved.