Bounds on 𝑟𝑟(𝐺 + 𝑒) in terms of 𝑟𝑟(𝐺) for Connected Graphs

S. Vimalajenifer

doi:https://doi.org/10.14445/22315373/IJMTT-V72I1P102

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 1 | Year 2026 | Article Id. IJMTT-V72I1P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I1P102

Bounds on 𝑟𝑟(𝐺 + 𝑒) in terms of 𝑟𝑟(𝐺) for Connected Graphs

S. Vimalajenifer

Received	Revised	Accepted	Published
16 Nov 2025	25 Dec 2025	11 Jan 2026	28 Jan 2026

Citation :

S. Vimalajenifer, "Bounds on 𝑟𝑟(𝐺 + 𝑒) in terms of 𝑟𝑟(𝐺) for Connected Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 1, pp. 13-15, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I1P102

Abstract

Let 𝐺(𝛤,𝛦) be a simple, connected, and undirected graph. A radial radio labeling of 𝐺, 𝜓:𝛤 → {1,2,3,…} is a function satisfying the condition for any two distinct vertices 𝑢 and 𝑣 that: 𝑑(𝑢,𝑣) + |𝜓(𝑢) − 𝜓(𝑣)| ≥ 1 + 𝑟𝑎𝑑(𝐺), where d(𝑢,𝑣) denotes the distance between the vertices 𝑢 and 𝑣, and 𝑟𝑎𝑑(𝐺) is the radius of the graph 𝐺. The 𝑠𝑝𝑎𝑛 of a radial radio labeling is the maximum integer that assigns to a vertex and 𝑟𝑎𝑑𝑖𝑎𝑙 𝑟𝑎𝑑𝑖𝑜 𝑛𝑢𝑚𝑏𝑒𝑟, 𝑟𝑟(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.

Keywords

Radial radio labeling, Radial Radio number, Graph labeling, Frequency assignment.

References

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