Radio number of trees
Devsi Bantva, Samir Vaidya, Sanming Zhou

TL;DR
This paper investigates the radio number of trees, establishing conditions for achieving bounds and determining the radio number for specific tree families, advancing understanding of graph labelings.
Contribution
It provides necessary and sufficient conditions for lower bounds and an upper bound on the radio number of trees, and calculates the radio number for three tree families.
Findings
Established conditions for bounds on the radio number of trees.
Derived an upper bound on the radio number of trees.
Determined the radio number for three specific families of trees.
Abstract
A radio labeling of a graph is a mapping such that for every pair of distinct vertices of , where is the diameter of and the distance between and in . The radio number of is the smallest integer such that has a radio labeling with . We give a necessary and sufficient condition for a lower bound on the radio number of trees to be achieved, two other sufficient conditions for the same bound to be achieved by a tree, and an upper bound on the radio number of trees. Using these, we determine the radio number for three families of trees.
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