New Families of 4-Total Prime Cordial Graph

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 u; v ∈ V , assign the label
gcd{f(u), f(v)}. f is called k-total prime cordial labeling of G if |t_f (i) - t_f (j)| ≤ 1, i, j ∈ {1, 2, ... , k} where t_f (x) denotes the total number of vertices and the edges labeled 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 some graphs like triangular ladder and armed crown, subdivision of jelly fish and subdivision of triangular ladder.

Key words and phrases. triangular ladder, armed crown, jelly fish.

2000 Mathematics Subject Classification. 05C78