Mathematics and Computational Sciences

Balanced Fermatean quadripartitioned neutrosophic fuzzy graphs and its application

Document Type : Original Article

Authors

Divya Venkatesan 1
Jesintha Rosline Jesuraj 1
Manikanda Prabhu Subramanian 2

1 epartment of Mathematics, Auxilium College (Autonomous), Affiliated to Thiruvalluvar University, Vellore Dist., Tamil Nadu, India.

2 Department of Mathematics, St. Joseph’s College of Engineering, OMR, Chennai 600119, Tamil Nadu, India.

https://doi.org/10.30511/mcs.2026.735274
Abstract
This article presents and investigates the novel model of a balanced Fermatean Quadripartitioned Neutrosophic Fuzzy Graphs, based on density functions. We examine the intrinsic properties of these graphs, focusing on the necessary conditions for Fermatean Quadripartitioned Neutrosophic Fuzzy Graphs (FQNFG) to achieve balance, particularly under self-complementary, complete, and strong graph characteristics. Additionally, we analyze the properties of FQNFG complements, providing insights into their structural relationships and transformations. Finally, we apply this theoretical foundation to model student performance, addressing uncertainties and complexities in educational data. Leveraging balanced FQNFGs provides clearer and fairer insights into student performance, enabling targeted interventions and supporting more effective with equitable educational practices.

Keywords

Fermatean neutrosophic graph (FNG)
Density of FNG
Balanced FNG
Fermatean quadripartitioned neutrosophic graph
Subjects
[1] Ajay, D. & Chellamani, P. (2020). Pythagorean Neutrosophic Fuzzy Graphs. International Journal of Neutrosophic Science, 11, 108–114.
[2] Ajay, D. & Chellamani, P. (2022). Operations on Pythagorean neutrosophic graphs. AIP Conference Proceedings, 2516, 200028. 
[3] Ajay, D., Chellamani, P., Rajchakit, G., Boonsatit, N., & Hammachukiattikul, P. (2022). Regularity of Pythagorean neutrosophic graphs with an illustration in MCDM. AIMS Mathematics, 5, 9424–9442. 
[4] Ajay, D., John Borg, S., & Chellamani, P. (2022). Domination in Pythagorean neutrosophic graphs with an application in fuzzy intelligent decision making. International Conference on Intelligent and Fuzzy Systems, Springer, pp. 667–675. 
[5] Akram, M. & Dudek, W. A. (2013). Intuitionistic fuzzy hypergraphs with applications. Information Sciences, 218, 182–193. 
[6] Akram, M., Karunambigai, M. G., Palanivel, K. & Sivasankar, S. Balanced bipolar fuzzy graphs. Journal of Advanced Research in Pure Mathematics. 
[7] Ali, M., Khan, A., Saeed, M. & Smarandache, F. (2021). Fermatean neutrosophic fuzzy sets and their applications in decision-making. Neutrosophic Sets and Systems, 44, 327–345. 
[8] Amanathulla, S., Bera, B. & Pal, M. (2021). Balanced picture fuzzy graphs with application. Artificial Intelligence Review, 54(7), 5255–5281. 
[9] Belnap, N. D. (1977). A useful four-valued logic. Modern uses of multiple-valued logic, Dordrecht: Springer. 
[10] Broumi, S., Sundareswaran, R., Shanmugapriya, M., Chellamani, P., Bakali, A. & Talea, M. (2023). Determination of various factors to evaluate a successful curriculum design using interval-valued Pythagorean neutrosophic graphs. Soft Computing, 1–20. 
[11] Broumi, S., Sundareswaran, R., Shanmugapriya, M., Bakali, A., & Talea, M. (2022). Theory and Applications of Fermatean Neutrosophic Graphs. Neutrosophic Sets and Systems, 50, 248–286. 
[12] Broumi, S., Sivasankar, S., Bakali, A. & Talea, M. (2022). Balanced neutrosophic graphs. Neutrosophic Sets and Systems, 50. 
[13] Broumi, S., Sivasankar, S., Bakali, A., Talea, M. (2024). Balanced neutrosophic Fermatean graphs with applications. Analytical Decision Making and Data Envelopment Analysis: Advances and Challenges, 413–431. 
[14] Chellamani, P. & Ajay, D. (2021). Pythagorean neutrosophic Dombi fuzzy graphs with an application to MCDM. Neutrosophic Sets and Systems, 47, 411–431. 
[15] Chellamani, P., Ajay, D., Al-Shamiri, M. M. & Ismail, R. (2023). Pythagorean neutrosophic planar graphs with an application in decision-making. Computers, Materials and Continua, 75. 
[16] Divya, V. & Jesintha Rosline, J. (2025). Fermatean Quadripartitioned Neutrosophic Fuzzy Graph. Reliability: Theory and Applications, 3(86).
[17] Divya, V. & Jesintha Rosline, J. (2025). Regularity of Fermatean Quadripartitioned Neutrosophic Fuzzy Graph. Intelligent and Fuzzy Systems, LNNS, 1531, 39–47. 
[18] Hussain, S. S., Muhiuddin, G., Durga, N. & Al-Kadi, D. (2021). New concepts on quadripartitioned bipolar single-valued neutrosophic graph. CMES-Computer Modeling in Engineering and Sciences, 130(1), 559–580. 
[19] Hussain, S. S., Rashmanlou, H., Mofidnakhaei, F., Hussain, J., Sahoo, S. & Broumi, S. (2022). Quadipartitioned Neutrosophic Graph Structures. Neutrosophic Sets and Systems. 
[20] Karunambigai, M. G., Akram, M., Sivasankar, S. & Palanivel, K. (2013). Balanced intuitionistic fuzzy graphs. Applied Mathematical Sciences, 7(51), 2501–2514. 
[21] Muhiuddin, G., Hussain, S. S. & Nagarajan, D. (2025). Quadripartitioned bipolar neutrosophic competition graph with novel application. Neutrosophic Sets and Systems. 
[22] Naz, S., Ashraf, S. & Akram, M. (2018). A novel approach to decision making with Pythagorean fuzzy information. Mathematics, 6, 95. 
[23] Parvathi, R. & Karunambigai, M. G. (2006). Intuitionistic fuzzy graphs. Computational Intelligence, Theory and Applications, Springer, Berlin, pp. 139–150. 
[24] Rashmanlou, H. & Pal, M. (2013). Balanced interval-valued fuzzy graphs. Journal of Physical Sciences, 17(1), 43–57. 
[25] Rashmanlou, H., Durga, N., Rahmonlou, H., Ghorai, G., Castillo, O. (2025). Novel supply chain decision-making model under m-polar quadripartitioned neutrosophic environment. Journal of Applied Mathematics and Computing, 71(1), 1051–1076. 
[26] Senapati, T. & Yager, R. R. (2019). Fermatean fuzzy sets. Intelligence and Humanized Computing, 11, 663–674. 
[27] Shil, B., Das, R., Das, S., Tripathy, B. C. & Granados, C. (2022). Degree, order and size of single-valued quadripartitioned neutrosophic graph. BISTUA Revista de la Facultad de Ciencias Basicas, 20(1), 63–69. 
[28] Sivasankar, J., and S. Jackson. Two-person games induced by pentapartitioned Neutrosophic Payoffs. Mathematics and Computational Sciences (2025): e733024. 
[29] Sunday Emmanuel Fadugba, Karpaha, John Robinson P, and Chandrasekar. Intuitionistic complex Fuzzy sets in decision support systems: A choquet operated data mining-ANN approach. Mathematics and Computational Sciences (2026): e733627.
[30] Talal AL-Hawary (2011). Complete fuzzy graphs. International Journal of Mathematics Combinatorics, 4, 26–34.
[31] Wilson Arul Prakash S, Gopal, John Robinson P, and Sumithra, An integrated eigenvalue based neural network approach for MAGDM with intuitionistic Fuzzy sets. Mathematics and Computational Sciences (2026): e733634.
[32] Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.
Mathematics and Computational Sciences
Volume 7, Issue 2
Spring 2026
Pages 215-227

  • Receive Date 13 November 2025
  • Revise Date 21 April 2026
  • Accept Date 26 April 2026

Home

Submit Manuscript

Reviewers

Contact Us