ON RAINBOW ANTIMAGIC COLORING OF SNAIL GRAPH(Sn), COCONUT ROOT GRAPH (Crn,m), FAN STALK GRAPH (Ktn) AND THE LOTUS GRAPH(Lon)

Abstract

Rainbow antimagic coloring is a combination of antimagic labeling and rainbow coloring. Antimagic labeling is labeling of each vertex of the graph G with a different label, so that each the sum of the vertices in the graph has a different weight. Rainbow coloring is part of the rainbow-connected edge coloring, where each graph G has a rainbow path. A rainbow path in a graph G is formed if two vertices on the graph G do not have the same color. If the given color on each edge is different, for example in the function fit is colored uv with a weight w(uv), it is called rainbow antimagic coloring. Rainbow antimagic coloring has a condition that every two vertices on a graph cannot have the same rainbow path. The minimum number of colors from rainbow antimagic coloring is called the rainbow antimagic connection number, denoted by rac(G). In this study, we analyze the rainbow antimagic connection number of snail graph (Sn), coconut root graph (CRn,m), fan stalk graph (Ktn) and lotus graph (Lon).