On the study of Rainbow Antimagic Coloring of Special Graphs

Abstract

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.