On Radio Number of Caterpillars
Abstract
A radio labeling of a graph πΊ is a function π from the vertex set π(πΊ) to the set of non-negative integers such that |π(π’) β π(π£)| β₯ diam(πΊ)+1βππΊ(π’,π£), where diam(πΊ) and ππΊ(π’,π£) are the diameter of πΊ and the distance between π’ and v in πΊ, respectively. The radio number rn(πΊ) of πΊ is the smallest number π such that πΊ has radio labeling with max{π(π£):π£ β π(πΊ)} = π. A tree π is called a caterpillar if it has a path π of maximum length such that all the vertices other than the path π are at most distance 1 from the path π. In this paper, we determine the radio number of some special types of caterpillars.
Fields of Study & Subjects
Graph Labeling and Dimension Problems
Advanced Graph Theory Research
Graph theory and applications
Publication details
- Journal / source
- International Journal of Mathematics Trends and Technology
- Volume
- 72
- Issue
- 2
- Pages
- 6β18
- Publication date
- 25 February 2026
- Language
- EN