Radio labelling of two-branch trees

Devsi Bantva, Samir Vaidya and Sanming Zhou

Applied Mathematics and Computation, 2025, vol. 487, issue C

Abstract: A radio labelling 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, where diam(G) is the diameter of G and d(u,v) is the distance between u and v in G. The radio number rn(G) of G is the smallest integer k such that G admits a radio labelling f with max⁡{f(v):v∈V(G)}=k. The weight of a tree T from a vertex v∈V(T) is the sum of the distances in T from v to all other vertices, and a vertex of T achieving the minimum weight is called a weight centre of T. It is known that any tree has one or two weight centres. A tree is called a two-branch tree if the removal of all its weight centres 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 improves a known lower bound for general trees. We also give a necessary and sufficient condition for this improved lower bound to be achieved. Using these results, we determine the radio number of two families of level-wise regular two-branch trees.

Keywords: Graph colouring; Radio labelling; Radio number; Trees; Level-wise regular trees (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:487:y:2025:i:c:s0096300324005587

DOI: 10.1016/j.amc.2024.129097

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