Quotient-4 Cordial Labeling of Some Unicyclic Graphs and Some Corona of Ladder 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 , i j 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 unicyclic graphs such as (C_n; K_1,2), C_m(1,2…m), (C_n(2P_m)) and some corona of ladder graphs such as (OL( )  K₁ ), (CL( )  K₁ ), (SL( )  K₁ ), (ML( )  K₁ ), (CRL( )  K₁), (PL( )  K₁ ) , (PCL( )  K₁ ) and (HL( )  K₁ ) proved to be quotient-4 cordial graphs.