On Radio Number of Caterpillars

Alamgir Rahaman Basunia

doi:https://doi.org/10.14445/22315373/IJMTT-V72I2P102

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 2 | Year 2026 | Article Id. IJMTT-V72I2P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I2P102

On Radio Number of Caterpillars

Alamgir Rahaman Basunia

Received	Revised	Accepted	Published
07 Dec 2025	15 Jan 2026	06 Feb 2026	21 Feb 2026

Citation :

Alamgir Rahaman Basunia, "On Radio Number of Caterpillars," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 2, pp. 6-18, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I2P102

Abstract

A radio labeling of a graph 𝐺 is a function 𝑓 from the vertex set 𝑉(𝐺) to the set of non-negative integers such that |𝑓(𝑢) − 𝑓(𝑣)| ≥ diam(𝐺)+1−𝑑𝐺(𝑢,𝑣), where diam(𝐺) and 𝑑𝐺(𝑢,𝑣) are the diameter of 𝐺 and the distance between 𝑢 and v in 𝐺, respectively. The radio number rn(𝐺) of 𝐺 is the smallest number 𝑘 such that 𝐺 has radio labeling with max{𝑓(𝑣):𝑣 ∈ 𝑉(𝐺)} = 𝑘. A tree 𝑇 is called a caterpillar if it has a path 𝑃 of maximum length such that all the vertices other than the path 𝑃 are at most distance 1 from the path 𝑃. In this paper, we determine the radio number of some special types of caterpillars.

Keywords

Caterpillar graph, Radio number, Span of a function.

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