On (a, d)-distance antimagic graphs

Let G = (V,E) be a graph of order n. Let f : V → {1, 2, . . . , n} be a bijection. For any vertex v ∈ V , the neighbor sum ∑u∈N(v) f(u) is called the weight of the vertex v and is denoted by w(v). If w(v) = k, (a constant) for all v ∈ V , then f is called a distance magic labeling with magic constant k. If the set of vertex weights forms an arithmetic progression {a, a+ d, a+2d, . . . , a+ (n− 1)d}, then f is called an (a, d)distance antimagic labeling and a graph which admits such a labeling is called an (a, d)-distance antimagic graph. In this paper we present several results on (a, d)-distance antimagic graphs.