On consecutive magic graphs

Abstract

Let G be a graph of order p and size q. A vertex-magic total labeling is an assignment of the integers 1,2,…,p+q to the vertices and the edges of G, so that at each vertex, the vertex label and the labels on the edges incident at that vertex, add to a fixed constant, called the magic constant. Such a labeling is a-vertex consecutive magic if the set of labels of the vertices is {a+1,a+2,…,a+p} and is b-edge consecutive magic if the set of labels of the edges is {b+1,b+2,…,b+q}. In this paper, we find some results on a-vertex consecutive magic graphs.