Quotient-4 Cordial Labeling of Some Ladder Graphs

Abstract

Let G (V, E) be a simple graph with p vertices and q edges. Let φ: V (G)  Z₅ – {0} be a function and *: E(G) Z₄ by *(uv)= (modulo 4) where (u) (v). If |v_φ(i) – v_φ(j)| ≤ 1, , j , i j  and |e_φ(k) – e_φ(l)| ≤ 1, , ,  then φ is Quotient-4 cordial labeling of G, where v_φ(x) and e_φ(y) denote the number of vertices labeled with x and the number of edges labeled with y. Here some types of ladder graphs are proved to be quotient-4 cordial graphs.