Radio labelling of two-branch trees
Devsi Bantva, Samir Vaidya, Sanming Zhou

TL;DR
This paper establishes a sharp lower bound for the radio number of two-branch trees, improves upon previous bounds for general trees, and characterizes when this bound is tight, with applications to specific tree families.
Contribution
It introduces a precise lower bound for the radio number of two-branch trees and provides conditions for its attainment, advancing understanding of graph radio labelling.
Findings
Derived a sharp lower bound for two-branch trees' radio number.
Provided necessary and sufficient conditions for achieving the bound.
Determined the radio number for specific level-wise regular two-branch trees.
Abstract
A radio labelling of a graph is a mapping such that for every pair of distinct vertices of , where is the diameter of and is the distance between and in . The radio number of is the smallest integer such that admits a radio labelling with . The weight of a tree from a vertex is the sum of the distances in from to all other vertices, and a vertex of achieving the minimum weight is called a weight center of . It is known that any tree has one or two weight centers. A tree is called a two-branch tree if the removal of all its weight centers results in a forest with exactly two components. In this paper we obtain a sharp lower bound for the radio number of two-branch trees which…
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Advanced Graph Theory Research
