Some distance antimagic labeled graphs
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2016
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Abstract. 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 wf (v) = P x∈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 fk : V (G) −→ {1 + k, 2 + k, . . . , n + k} by fk(x) = f(x) + k. If wfk (u) 6= wfk (v) for every pair of vertices u, v ∈ 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 rPn, generalised Petersen graph P(n, k), n ≥ 5, Harary graph H4,n for n 6= 6 and also prove that join of these graphs is distance antimagic.