Cauchy: Jurnal Matematika Murni dan Aplikasi (Nov 2021)

On Rainbow Vertex Antimagic Coloring of Graphs: A New Notion

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

DOI
https://doi.org/10.18860/ca.v7i1.12796
Journal volume & issue
Vol. 7, no. 1
pp. 64 – 72

Abstract

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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 ( ).

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