On the k-edge magic graphs

Let G be a graph with vertex set V and edge set E such that |V|=p and |E|=q. We denote this graph by (p, q)-graph. For integers k⩾0, define a one-to-one map f from E to {k,k+1,…,k+q−1} and define the vertex sum for a vertex v as the sum of the labels of the edges incident to v. If such an edge labeling induces a vertex labeling in which every vertex has a constant vertex sum (mod p), then G is said to be k-edge magic (k-EM). In this paper, we consider some specific graphs and obtain some results for them to be k-EM.