On Rainbow Antimagic Coloring of Joint Product of Graphs

Brian Juned Septory, Liliek Susilowati, Dafik Dafik, M. Venkatachalam

Abstract


Let  be a connected graph with vertex set  and edge set . A bijection  from  to the set  is a labeling of graph . The bijection  is called rainbow antimagic vertex labeling if for any two edge  and  in path , where  and . Rainbow antimagic coloring is a graph  which has a rainbow antimagic labeling. Thus, every rainbow antimagic labeling induces a rainbow coloring G where the edge weight  is the color of the edge . The rainbow antimagic connection number of graph  is the smallest number of colors of all rainbow antimagic colorings of graph , denoted by . In this study, we studied rainbow antimagic coloring and have an exact value of rainbow antimagic connection number of joint product of graph  where  is graph , graph , graph , graph  and graph .


Keywords


antimagic labeling; joint product of graphs; rainbow coloring; rainbow antimagic connection number

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DOI: https://doi.org/10.18860/ca.v7i4.17471

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