GROUP S₃ CORDIAL REMAINDER LABELING OF SUBDIVISION OF GRAPHS

GROUP S₃ CORDIAL REMAINDER LABELING OF SUBDIVISION OF GRAPHS

Let G = (V (G), E(G)) be a graph and let g : V (G) → S₃ 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 S₃ cordial remainder labeling of G if |v_g(i)-v_g(j)| ≤ 1 and |e_g(1)-e_g(0)| ≤ 1, where v_g(j) denotes the number of vertices labeled with j and e_g(i) denotes the number of edges labeled with i (i = 0, 1). A graph G which admits a group S₃ cordial remainder labeling is called a group S₃ cordial remainder graph. In this paper, we prove that subdivision of graphs admit a group S₃ cordial remainder labeling.