GROUP S3 CORDIAL SUM DIVISOR LABELING OF SOME DERIVED GRAPHS

Abstract

Let G = (V (G), E(G)) be a graph and let h : V (G) → S₃ be a function. For each edge uv assign the label 1 if 2 divides (O(h(u))+O(h(v))) and 0 otherwise. The function h is called a Group S₃ cordial sum divisor labeling of G if |v_h(i) − v_h(j)| ≤ 1 and |e_h(1) − e_h(0)| ≤ 1 where v_h(k) denote the number of vertices labeled with k, k ∈ S₃ and e_h(1) and e_h(0) denote the number of edges labeled with 1 and 0 respectively. A graph G which admits a Group S₃ cordial sum divisor labeling is called a Group S₃ cordial sum divisor graph. In this paper, we investigate the Group S₃ cordial sum divisor labeling of some derived graphs.