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 |vφ(i) – vφ(j)| ≤ 1, , j, ij where vφ(x) denote the number of vertices labeled with x and |eφ(k) – eφ(l)| ≤ 1, ,,, where eφ(y) denote the number of edges labeled with y. Here some caterpillar graphs such as star graph (Sn), Bistar graph (Bn,n), Pn [N] graph, Pn [No] graph, Pn [Ne] graph, Twig graph (Tm), (Pn   K1, r), S(Sn), S(Bn,n), S(Pn [N]), S(Pn [No]), S(Pn [Ne]), S(Tm) and S(Pn   K1, r) graph proved to be quotient-4 cordial graphs