Bounds on π‘Ÿπ‘Ÿ(𝐺 + 𝑒) in terms of π‘Ÿπ‘Ÿ(𝐺) for Connected Graphs

International Journal of Mathematics Trends and Technology 2026 Open access

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Authors: S. Vimalajenifer
DOI: 10.14445/22315373/ijmtt-v72i1p102
Cited by: 0

Abstract

Let 𝐺(𝛀,𝛦) be a simple, connected, and undirected graph. A radial radio labeling of 𝐺, πœ“:𝛀 β†’ {1,2,3,…} is a function satisfying the condition for any two distinct vertices 𝑒 and 𝑣 that: 𝑑(𝑒,𝑣) + |πœ“(𝑒) βˆ’ πœ“(𝑣)| β‰₯ 1 + π‘Ÿπ‘Žπ‘‘(𝐺), where d(𝑒,𝑣) denotes the distance between the vertices 𝑒 and 𝑣, and π‘Ÿπ‘Žπ‘‘(𝐺) is the radius of the graph 𝐺. The π‘ π‘π‘Žπ‘› of a radial radio labeling is the maximum integer that assigns to a vertex and π‘Ÿπ‘Žπ‘‘π‘–π‘Žπ‘™ π‘Ÿπ‘Žπ‘‘π‘–π‘œ π‘›π‘’π‘šπ‘π‘’π‘Ÿ, π‘Ÿπ‘Ÿ(𝐺) is the minimum span taken overall radial radio labelings of G. This paper presents relationships between the radial radio number of a graph and its super-graph obtained by adding a new edge under some constraints.

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
1
Pages
13–15
Publication date
28 January 2026
Language
EN