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.

Keywords

• antimagic labeling
• rainbow coloring
• rainbow antimagic connection number
• special graphs