On the Radio k-chromatic Number of Some Classes of Trees

Abstract

Radio k-coloring of a graph G is an assignment f of positive integers (colors) to the vertices of G such that for any two distinct vertices u and v of G, the difference between their colors is at least 1 + k- d(u, v). The span rc<inf>k</inf>(f) of f is the largest number assigned by f. The radio k-chromatic number rc<inf>k</inf>(G) is min{rck(f):fis a radiok-coloring ofG}. When k= diam(G) , f is called a radio coloring of G and the corresponding radio k-chromatic number is known as the radio number of G. In this paper, we determine the radio number of some classes of trees. Also, we find the radio d-chromatic number of infinitely many trees and graphs of arbitrarily large diameter constructed from trees of diameter d in some subclasses of the above classes. © 2020, Springer Nature India Private Limited.