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Open Access ·Peer-reviewed·ISSN (Online): 2169-0103·ISSN (Print): 0252-2667

WoS  JIF 2026 : 0.4 (Q4)

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Open Access Research Article

Graph product techniques for cordial labeling on cubic root graph structures

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pp. 1479–1488Vol. 47Issue 4April 2026DOI: 10.47974/JIOS-2191XML
Received:
01 Nov 2025
Published Online:
04 Apr 2026
Article type:
Research Article
Language:
EN
Article no.:
JIOS-2191
Pages:
1479–1488

Abstract

Graph labeling is the term used to describe the procedure of giving unique identifiers. Graph attributing is a method for modeling real-world problems in industries such as circuit design, surveillance technology, and telecommunications networks. A graph is characterized as possessing cubic roots cordial labeling if each node is designated with either the value 1, δ or δ2 or another specified integer. The derived set containing  the value 1 or another integer, the mathematical conditions  η (k) − η (w)| ≤ 1 and | ξ (k) − ξ (w)| ≤ 1, k ≠ w and k, w ∈ {1, δ, δ2} where  η (k) and ξ (k) are represents the aggregated vertices and edges assigned in  k ∈ {1, δ, δ2}. Labeled graphs prove to be immensely beneficial across a variety of mathematical frameworks, including domains such as cyber security and radar code formulation. The application of cordial labeling has been demonstrated to provide significant advantages in the context of signal processing  channels and challenges associated with specific code word design. The idea of cubic roots cordial labeling has attracted a lot of academic attention among various labeling techniques, unique structural characteristics and capacity to depict a fair flow of information within linked networks. The investigation of the behavior of cubic roots cordial labeling in relation to graph operations is currently receiving extensive scholarly examination, particularly concerning path graphs, despite its critical relevance. This paper explore the cordial labeling of cubic product graphs generated from the combination of two path graphs. The four fundamental graph operations on which we particularly focus on activities, we analyze the specific conditions to possess cubic roots cordial labeling.

Keywords

Subject Classifications

05C9005C78

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