Union Of 4-Total Prime Cordial Graph G With The Bistar Bn,N

Abstract

Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map where k ∈ N is a variable and k > 1. For each edge uv, assign the label gcd(f (u), f (v)). The map f is called a k- Total prime cordial labeling of G if |tpf (i) − tpf (j)| ≤ 1, i, j ∈
 {1, 2, · · · , k} where tpf (x) denotes the total number of vertices and the edges labelled with x. A graph with a k-total prime cordial labeling is called k-total prime cordial graph. In this paper we investigate the 4-total prime cordial labeling of G ∪ Bn,n, where G has a 4-total prime cordial labeling and Bn,n is a bistar.