On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion

Marsidi Marsidi, Ika Hesti Agustin, Dafik Dafik, Elsa Yuli Kurniawati

Abstract


All graph in this paper are simple, finite, and connected. Let  be a labeling of a graph . The function  is called antimagic rainbow edge labeling if for any two vertices  and , all internal vertices in path  have different weight, where the weight of vertex is the sum of its incident edges label. The vertex weight denoted by  for every . If G has a antimagic rainbow edge labeling, then  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 ( ).


Keywords


antimagic rainbow vertex connnection; antimagic rainbow vertex connection number; antimagic labeling; rainbow vertex connection

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DOI: https://doi.org/10.18860/ca.v7i1.12796

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