Sum 3-equitable labelling in wheel graph
Purnika Sijwali2024177951.purnika@pg.sharda.ac.inDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , Sweta Srivastavsweta.srivastav@sharda.ac.inDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , *Sangeeta GuptaCorresponding authorsangeeta147@gmail.comDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , Rachna Khuranarachnaakshaj@gmail.comDepartment of Applied SciencesSharda University AgraAgra, Uttar Pradesh, 201310, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Jul 2026
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2802
- Pages:
- 3315–3321
Abstract
In this paper, we investigate a MATLAB program to demonstrate the behavior of wheel graphs under sum 3-equitable labeling. A vertex labeling ζ of a graph W, defined as a bijection from the vertex set V(W) to the set {0, 1, 2…., m−1}, induces an edge labeling ζ*
given by:
ζ * (qr) = {0 if ζ(q) + ζ(r) ≡ 0(mod3) 1 if ζ(q) + ζ(r) ≡ 1(mod3) 2 if ζ(q) + z(r) ≡ 2(mod3)
and |eζ (l) – eζ (k)| ≤ 1 for all 0 ≤ l, k ≤ 2. A graph which preserves sum 3-equitable labeling is called a sum 3- equitable graph.
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References
[1] J. A. Gallian, “A dynamic survey of graph labeling,” Electron. J. Combin., Dynamic Survey DS6 (2018).
[2] A. Rosa, “On certain valuations of the vertices of a graph,” in Theory of Graphs. New York, USA: Gordon and Breach, pp. 349–355 (1967).
[3] D. B. West, Introduction to Graph Theory, 2nd ed. Upper Saddle River, NJ, USA: Prentice Hall (2001).
[4] J. Gross and J. Yellen, Graph Theory and Its Applications, 2nd ed. Boca Raton, FL, USA: Chapman & Hall/CRC (2005).
[5] F. Harary, Graph Theory. Reading, MA, USA: Addison-Wesley (1994).
[6] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications. New York, USA: Springer (2008).
[7] W. Stallings, Data and Computer Communications, 8th ed. Upper Saddle River, NJ, USA: Pearson Prentice Hall (2007).
[8] P. Kairouz and H. Brendan McMahan, “Advances and open problems in federated learning,” Found. Trends Mach. Learn., vol. 14, no. 1–2, pp. 1–210 (2021).
[9] S. K. Vaidya and N. J. Kothari, “Prime labeling for some graphs,” J. Discrete Math. Sci. Cryptogr., vol. 13, no. 1, pp. 17–24 (2010).
[10] K. A. Germina and N. K. Sudev, “On certain types of graph labelings,” Journal of Combinatorial Mathematics and Combinatorial Computing, vol. 75, pp. 57–64 (2010).
