Let G be a graph of order n. A bijection f : V(G) → {1,2,… ,n} is said to be distance antimagic if for every vertex v the vertex weight defined by w_f(ν) = ∑_(x∈N(ν) )f(x) is distinct. The graph which admits such a labeling is called a distance antimagic graph. For a positive integer k, define f_k : V(G) → {1+k,2+k,… ,n+k} by f_k(x) = f(x) + k. If w_(f_k) (u) ≠ w_(f_k) (v) for every pair of vertices u, v ∈ V, for any k ≥ 0 then / is said to be an arbitrarily distance antimagic labeling and the graph which admits such a labeling is said to be an arbitrarily distance antimagic graph. In this paper, we provide arbitrarily distance antimagic labelings for rP_n, generalised Petersen graph P(n,k), n ≥ 5, Harary graph H_(4,n) for n ≠ 6 and also prove that join of these graphs is distance antimagic.
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