On the study of Rainbow Antimagic Coloring of Special Graphs

Dafik Dafik (Jember University)
Riniatul Nur Wahidah (Jember University)
Ermita Rizki Albirri (Jember University)
Sharifah Kartini Said Husain (Institute for Mathematical Research, University Putra Malaysia)

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 . The bijective function  is said to be a labeling of graph where  is the associated weight for edge . If every edge has different weight, the function  is called an edge antimagic vertex labeling. A path  in the vertex-labeled graph , with every two edges  satisfies  is said to be a rainbow path. The function  is called a rainbow antimagic labeling of , if for every two vertices , there exists a rainbow  path. Graph  admits the rainbow antimagic coloring, if we assign each edge  with the color of the edge weight  . The smallest number of colors induced from all edge weights of edge antimagic vertex labeling is called a rainbow antimagic connection number of , denoted by . In this paper, we study rainbow antimagic connection numbers of octopus graph , sandat graph , sun flower graph , volcano graph  and semi jahangir graph Jn.