Group 3 S Cordial Remainder Labeling

Let G (V(G),E(G)) be a graph and let 3 g V: (G) S be a function. For each edge xy , assign the label r where r is the remainder when o g x ( ) is divided by o g y ( ) or o g y ( ) is divided by o g x ( ) according as o g x o g y ( ) ( ) or o g y o g x ( ) ( ) . The function g is called a group 3 S cordial remainder labeling of G if | ( ) ( ) | 1 g g v x v y and | (0) (1) | 1 g g e e , where ( ) g v x denotes the number of vertices labeled with x and () g e i denotes the number of edges labeled with i i ( 0,1) . A graph G which admits a group 3 S cordial remainder labeling is called a group 3 S cordial remainder graph. In this paper, we introduce the concept of group 3 S cordial remainder labeling. We prove that some standard graphs admit a group 3 S cordial remainder labeling.