Volume :7 , Issue :4 ,Page :104-123

Abstract :Let G be a connected graph with diameter diam(G ). The PVB - tree is a tree consisting of b branches at each vertex of all the p copies of the pa th V on v vertices and these paths are joined to the vertices of a path P on p vertices. This PVB tree contains pvb + pv + p vertices and pvb + pv + p – 1 edges. The radio number for G, denote d by rn(G), is the smallest integer k such that there exists a function ᅑ : V (G) → {0, 1, 2, · · · , k} with | ᅑ (u)− ᅑ (v)| ≥ diam(G)−d(u, v)+1 for a ll vertices u and v, where d(u, v) is the distance between u and v. We prove that the PVB - tree admits a radio labeling for all positive integers p ≥ 3, v ≥ 1 and b ≥ 1.