Some new families of 3-equitable prime cordial graphs

Abstract

Let G = (V(G), E(G)) be a graph. A 3-equitable prime cordial labeling of a graph G is a bijection f from V(G) to {1,2, ... V(G)} such that if an edge uv is assigned the label 1 if gcd (f(u), f(v)) =1 and the gcd (f(u) + f(v), f(u) – f(v)) = 1, lable 2 if gcd (f(u), f(v)) =1 and gcd (f(u) + f(v), f(u) – f(v)) = 1 and the label 0 otherwise, then the number of edges labeled with i and the number of edges labeled with j differ by at most 1 for 0 2), comb Pn+(n>2), ladder P2 x Pn, kite K(3,n) and slanting ladder SLn admit 3-equitable prime cordial labeling.