All graph in this paper are simple, finite, and connected. Let Â be a labeling of a graph . The function Â is called antimagic rainbow edge labeling if for any two vertices Â and , all internal vertices in path Â have different weight, where the weight of vertex is the sum of its incident edges label. The vertex weight denoted by Â for every . If G has a antimagic rainbow edge labeling, then Â is a antimagic rainbow vertex connection, where the every vertex is assigned with the color . The antimagic rainbow vertex connection number of , denoted by , is the minimum colors taken over all rainbow vertex connection induced by antimagic rainbow edge labeling of . In this paper, we determined the exact value of the antimagic rainbow vertex connection number of path ( ), wheel ( ), friendship ( ), and fan ( ).
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