On (a, d)-distance antimagic graphs.
S. Arumugam, N. Kamatchi · NOVA (University of Newcastle Australia) · 2012
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.