An Exact Determination of the Radio Number of Graph Hn for n≥15

Munawwar Hussain, M. Tariq Rahim, Zeeshan Saleem Mufti, Ali Tabraiz and Gamachu Adugna Ganati

Journal of Mathematics, 2026, vol. 2026, 1-10

Abstract: Suppose that G is a connected graph. For any two vertices u and v, let dG (u,v) denote the distance between u and v in G. The diameter of G is the maximum distance between any pair of vertices, and it is denoted by diamG. A multilevel distance labeling (or radio condition) for G is a function f that assigns to each vertex of G a positive integer such that for any distinct vertices u and v, du,v+fu−fv≥diamG+1. The largest positive integer in the range of f is called the span of f. The radio number of G is denoted by rnG, is the minimum span of a multilevel distance labeling for G. In this paper the multilevel distance labeling of Hn is calculated for every n≥15: rnHn=4n+2.

Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:1606937

DOI: 10.1155/jom/1606937

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