On rainbow antimagic coloring of graphs

Abstract

A rainbow antimagic coloring is one of new topics in graph theory. This topic is an expansion of rainbow coloring that is combined with antimagic labeling. The graphs are labeled with an antimagic labeling, and then the sum of vertex label have to obtain a rainbow coloring. The aim of the rainbow antimagic coloring research is to find the minimum number of color, called rainbow antimagic connection number, denoted by rac(G). In this research, we studied some simple graphs to be colored with rainbow antimagic coloring. The graphs we used are lollipop, stacked book, Dutch windmill, flowerpot and dragonfly. In this research, we aimed to develop new theorem. Based on the results, we got some theorems about rac(G) for the rainbow antimagic coloring. In addition, on some graphs that we use, we get rac(G) equal to rc(G), rainbow connection number. Instead, on the others, the value of rac(G) cannot reach the rc(G).