On Rainbow Antimagic Coloring of Joint Product of Graphs

Brian Juned Septory (Mathematics Department Airlangga University, Surabaya)
Liliek Susilowati (Mathematics Department Airlangga University, Surabaya)
Dafik Dafik (CoE Combinatorics and Graph, CGANT, University of Jember)
M. Venkatachalam (Department on Mathematics, Kongunadu Arts and Science College, Tamil Nadu)

CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 7, No 4 (2023): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

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 .