Distance Antimagic Labeling of the Join & Corona Product of two Graphs
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Date
2017
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AKCE International Journal of Graphs and Combinatorics
Abstract
Let G be a graph of order n. Let f∶ V (G)→{1, 2,..., n} be a bijection. The weight wf (v) of a vertex with respect to f is defined by wf (v)=∑ x∈ N (v) f (x). The labeling f is said to be distance antimagic if wf (u)≠ wf (v) for every pair of vertices u, v∈ V (G). If the graph G admits such a labeling then G is said to be a distance antimagic graph. In this paper we prove that Pm+ Pn, Pm+ Cn, Pm+ Wn and Cm+ Wn are distance antimagic. We have also proved that if G and H are distance antimagic graphs satisfying certain conditions, then G+ H is distance antimagic and if G is magic and H is arbirarily distance antimagic then G○ H is distance antimagic.
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Handa, A. K., Singh, T., Godinho, A., & Arumugam, S. Distance Antimagic Labeling of the Join & Corona Product of two Graphs.