Group 3 S Cordial Remainder Labeling

Abstract

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.