Quotient-4 Cordial Labeling Of Some Caterpillar And Lobster Graphs

Abstract

Let G (V, E) be a simple graph of order p and size q. Let φ: V (G) Z₅ – {0} be a function. For each edge set E (G) define the labeling *:E (G)Z₄ by *(uv)= (mod 4) where (u)(v). The function  is called Quotient-4 cordial labeling of G if |v_φ(i) – v_φ(j)| ≤ 1, , j, ij where v_φ(x) denote the number of vertices labeled with x and |e_φ(k) – e_φ(l)| ≤ 1, ,,, where e_φ(y) denote the number of edges labeled with y. Here some caterpillar graphs such as star graph (S_n), Bistar graph (B_n,n), P_n [N] graph, P_n [N_o] graph, P_n [N_e] graph, Twig graph (T_m), (P_n   K_{1, r}), S(S_n), S(B_n,n), S(P_n [N]), S(P_n [N_o]), S(P_n [N_e]), S(T_m) and S(P_n   K_{1, r}) graph proved to be quotient-4 cordial graphs.