Some results on k-edge-magic broken wheel graphs

Let G be a (p, q)-graph in which the edges are labeled k, k+1, . . . , k+q−1, where k ∈ Z. The vertex sum for a vertex v is the sum of the labels of the incident edges at v. If the vertex sums are constant modulo p, then G is said to be k-edge-magic. In this paper, we give necessary conditions for a family of regular broken wheel graphs to admit kedge- magic labelings. Consequently, we show that some of these conditions are also sufficient.