Sum 3-equitable labeling of fan graphs : Theoretical results and algorithmic approach
Simron Sharma2024143720.simron@pg.sharda.ac.inDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , Sangeeta Guptasangeeta147@gmail.comDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , *Sweta SrivastavCorresponding authorsweta.srivastav@sharda.ac.inDepartment of Mathematics & Data ScienceSharda School of Engineering & ScienceSharda UniversityGreater Noida, Uttar Pradesh, 201310, IndiaView full profile → , Deepti Guptadg.gupta399@gmail.comDepartment of MathematicsPatna CollegePatna UniversityBihar, 800001, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Dec 2025
- Published Online:
- 30 Sep 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2853
- Pages:
- 3353–3360
Abstract
The study explores the use of a MATLAB program to prove the theorem that fan graphs admit sum 3-equitable labeling. The labeling scheme is defined as a bijective transformation, which assigns integer values to the vertices of the graph. These values are then used to determine the edge values, which are computed on the sum of the values of the vertices the edge joins modulo three. This classification primarily requires the preservation of equitability, which means the edges labeled via the transformation must almost evenly lie in the three classes, such that the absolute value of edges in any two classes differs by no more than one.
Keywords
Subject Classifications
References
[1] G. S. Bloom and S. W. Golomb, “Applications of numbered undirected graphs,” Proc. IEEE, vol. 65, no. 4, pp. 562–570 (Apr. 1977), doi: 10.1109/PROC.1977.10517.
[2] I. Cahit, “On cordial and 3-equitable labellings of graphs,” Util. Math., vol. 37, pp. 189–197 (1990).
[3] S. Rathinakumar and K. M. Kathiresan, “3-equitable total labeling of graphs,” J. Combin. Math. Combin. Comput., vol. 113, pp. 155–163 (May 2020).
[4] S. Sadawarte and S. Srivastav, “On sum 3-equitable labeling of some graphs,” in Mathematical Modeling for Computer Applications, pp. 197–205 (2024), doi: 10.1002/9781394248438.ch11.
[5] S. Murugesan and J. Shiama, “Square difference 3-equitable labeling of some graphs,” Int. J. Comput. Appl., vol. 137, no. 13, pp. 1–4 (Mar. 2016), doi: 10.5120/ijca2016909018.
[6] I. Cahit, “Cordial graphs—a weaker version of graceful and harmonious graphs,” Ars Combinatoria, vol. 23, pp. 201–208 (1987).
[7] S. Murugesan, D. Jayaraman, and J. Shiama, “3-equitable prime cordial labeling of graphs,” Int. J. Appl. Inf. Syst., vol. 5, no. 9, pp. 1–4 (Jul. 2013), doi: 10.5120/ijais13-450974.
[8] S. Srivastav and S. Gupta, “Energy of some simple graphs: MATLAB approach,” Int. J. Comput. Sci. Inf. Secur., vol. 15, no. 9, pp. 7–9 (Sep. 2017).
[9] S. Gupta and S. Srivastav, “MATLAB algorithm for new results on energy of graphs,” Int. J. Comput. Sci. Inf. Secur., vol. 17, no. 3, pp. 14–17 (Mar. 2019).
[10] S. Srivastav and S. Gupta, “Results with MATLAB coding of middle graph of cycle and its related graphs in context of sum divisor cordial,” Int. J. Emerg. Trends Eng. Res., vol. 8, no. 2, pp. 398–401 (Feb. 2020), doi: 10.30534/ijeter/2020/2622020.
[11] F. Harary, Graph Theory. Reading, MA, USA: Addison-Wesley (1972).
[12] J. A. Gallian, “A dynamic survey of graph labeling,” Electron. J. Combin., vol. 17, Dynamic Survey DS6 (2010).
[13] U. Kumari, S. Mehra, V. Garg, and A. Sehgal, “Super graceful labeling of co-maximal subgroup graphs of some cyclic groups,” J. Discrete Math. Sci. Cryptogr., vol. 28, no. 6, pp. 2439–2453 (2025), doi: 10.47974/JDMSC-2316.
[14] A. Panchbhai, T. Singh, V. Kolekar, K. D. Bamane, N. J. Bhagyam, and S. Lakhampal, “Utilizing line graph construction in combinatorial analysis for network optimization,” J. Discrete Math. Sci. Cryptogr., vol. 29, no. 1, pp. 307–315 (2026), doi: 10.47974/JDMSC-2488.
