Further results on the radio number of trees

Let G be a finite, connected, undirected graph with diameter diam(G) and d(u, v) denote the distance between u and v in G. A radio labeling of a graph G is a mapping f:V(G)→{0,1,2,…} such that |f(u)−f(v)|≥diam(G)+1−d(u,v) for every pair of distinct vertices u, v of G. The radio number of G, denoted by rn(G), is the smallest integer k such that G has a radio labeling f with max⁡{f(v):v∈V(G)}=k. In this paper, we determine the radio number for three families of trees obtained by taking graph operation on a given tree or a family of trees.