LAUSR

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 $$rc_k(f)$$ of f is the largest number assigned by f. The radio k-chromatic number $$rc_k(G)$$ is $$\min \lbrace rc_k(f) : f \text { is a radio }k\text {-coloring of } G\rbrace $$. 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.