On product cordial labeling of helm graphs and their subdivisions : An algorithmic approach
Varsha Rathi2022401996.varsha@dr.sharda.ac.inDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityNoida, Uttar Pradesh, 201310, IndiaView full profile → , *Sweta SrivastavCorresponding authorsweta.srivastav@sharda.ac.inDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityNoida, Uttar Pradesh, 201310, IndiaView full profile → , Sangeeta Guptasangeeta.gupta@sharda.ac.inDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityNoida, Uttar Pradesh, 201310, IndiaView full profile →
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- Received:
- 01 Jan 2026
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2861
- Pages:
- 3453–3462
Abstract
This paper deals with product cordial labeling in graphs, with emphasis being placed on helm graphs and their subdivisions. Let G = (V, E) be a simple graph. Given a vertex labeling function f : V (G) → {0, 1}, we define an edge labeling function f ∗ : E(G) → {0, 1} given by f ∗(uv) = f (u)f (v). Graph G is called product cordial if the difference between the number of vertices labeled 0 and 1 and the number of edges labeled 0 and 1 is at most one. An algorithmic approach for the construction and testing of product cordial labelings is introduced in this paper. Based on our approach, we obtain product cordial labeling schemes for helm graphs and their subdivisions. Moreover, we provide sufficient conditions for the existence of such labelings for both graph classes. We show that helm graphs and their subdivisions indeed possess product cordial labelings based on the given scheme.
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References
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