Bitopological Harmonious Labeling of Some Star
Related Graphs

M. Subbulakshmi; S. Chandrakala; G. Siva Prijith

doi:https://doi.org/10.14445/22315373/IJMTT-V71I7P105

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 7 | Year 2025 | Article Id. IJMTT-V71I7P105 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I7P105

Bitopological Harmonious Labeling of Some Star Related Graphs

M. Subbulakshmi, S. Chandrakala, G. Siva Prijith

Received	Revised	Accepted	Published
22 May 2025	29 Jun 2025	14 Jul 2025	27 Jul 2025

Citation :

M. Subbulakshmi, S. Chandrakala, G. Siva Prijith, "Bitopological Harmonious Labeling of Some Star Related Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 7, pp. 44-48, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I7P105

Abstract

Bitopological harmonious labeling for a graph 𝐺 = (𝑉(𝐺),𝐸(𝐺)) with 𝑛 vertices, is an injective function f:𝑉(𝐺) → 2𝑋, where X is any non–empty set such that |𝑋| = 𝑚, 𝑚 < 𝑛 and {𝑓(𝑉(𝐺))} forms a topology on 𝑋, that induces an injective function 𝑓∗: 𝐸(𝐺) → 2𝑋∗ , defined 𝑏𝑦 𝑓∗(𝑢𝑣) = 𝑓(𝑢)∩ 𝑓(𝑣) for every 𝑢𝑣 ∈ 𝐸(𝐺) such that {𝑓∗(𝐸(𝐺))} forms a topology on 𝑋∗ where 𝑋∗ = 𝑋\{1,2,….,𝑚}. A graph that admits bitopological harmonious labeling is called a bitopological harmonious graph. In this paper, we discuss bitopological harmonious labeling of some star-related graphs.

Keywords

Bistar graph, Bitopological harmonious graph, Firecracker graph, Lilly graph, Spider graph.

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