A Study on Radio Labelling of Evolving Trees for Path $P_n$

Abstract

The term radio labelling of a graph G of diameter d means a function f which maps each vertex of G with a non-negative integer such that the condition $|f(x)-f(y)| \geqslant d + 1 - d(x,y)$, holds for $x,y\in G$, where d(x, y) represents the distance of x and y. The difference between the maximum and minimum values in f(V) is termed as the span of f. The smallest span amongst all radio labelling that would be permitted by G is termed as the radio number of the graph G. Here we investigate radio labelling problem for evolving trees of path $P_{n}$ and determine the radio number for several trees.