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

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... ling is called an (a, d)-distance antimagic graph. In this paper we present several results on (a, d)-distance antimagic graphs.