On The Rainbow Antimagic Connection Number of Some Wheel Related Graphs

Abstract

All graphs in this paper is connected and simple. Let ( ) be a connected and simple graph with vertices set and edge set . A bijection function * | ( )|+ is called an edge antimagic vertex labelling if for every ( ), the edge weight ( ) ( ) ( ) are all different. An edge antimagic labeling can generate a rainbow edge antimagic coloring if there is a rainbow path between every pair of vertices. The rainbow edge antimagic connection number of graph , denoted by ( ) is the smallest number of colors that are needed in order to make rainbow connected under the assignment of edge antimagic labelling. In this paper, we will study the existence of rainbow antimagic coloring its connection number of some wheel related graphs. We have found the values of the rainbow antimagic connection of flower graph and gear graph.