Author(s): A Sugumaran and P Vishnu Prakash

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< i < 2 and 0 < j < 2. If a graph has a 3-equitable prime cordial labeling, then it is called a 3-equitable prime cordial graph. In this paper, we have prove that the bistar B_n,n (n>2), comb P_n⁺(n>2), ladder P₂ x Pn, kite K(3,n) and slanting ladder SL_n admit 3-equitable prime cordial labeling.

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