Total prime labeling of some subdivision graphs

In this paper we investigate that the prime labeling for some subdivision graphs. Let G = (V, E) be a graph with ‘p’ vertices and ‘q’ edges. A bijection f: VUE to { 1, 2, 3, …….. (p + q) } is said to be total prime labeling if (i) for each edge e = uv, the labels assigned to u and v are relatively prime, (ii) for each vertex of degree at least 2, the gcd of the labels on the incident edges is one. A graph which admits total prime labeling is called total prime graph. We prove that the graph obtained by subdivision of pendent edges of Stars, Bistars, Coconut trees and Kite graphs are all total prime graphs.