UPPER BOUNDS ON THE RADIO NUMBER OF SOME TREES
Prabhakar T. Venkata, Subba Reddy, Kailasam Viswanathan Iyer · International Journal of Pure and Apllied Mathematics · 2011
Let G be a simple,connected and undirected graph with diameter d. For a positive integer k (� d), a radio k-labeling f of G is an assignment of non-negative integers, called labels to the vertices of G such that if u,v 2 V (G) are distinct then d(u,v) + j f(u) − f(v)jk + 1 where d(u,v) is the distance between u and v. The maximum label (positive integer) assigned by f to some vertex of G is called the span of f. The radio number of G denoted by rn(G) is the minimum span over all radio d-labelings of G. In this paper, we prove an upper bound for the radio number of binomial tree, Fibonacci trees and uniform caterpillar.