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.