Some Distance Antimagic Labeled Graphs

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) (v) = Sigma(x is an element of N(v)) 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(fk) (u) not equal w(fk) (v) for every pair of vertices u, v is an element of V, for any k >= 0 then f 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,H- n for n not equal 6 and also prove that join of these graphs is distance antimagic.