Algebraic graph theory in secure communication design
Tanveer Ahmad Wanitanveer.ahmad@niu.edu.inDepartment of PhysicsNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Nitinkumar M. Patelnmpatel.gen.hcet@gokuluniversity.ac.inFaculty of EngineeringGokul Global UniversitySidhpur, Gujarat, 384151, IndiaView full profile → , Kotte Navyakottenavya@yahoo.comCentre for Multidisciplinary ResearchAnurag UniversityHyderabad, Telangana, 500088, IndiaView full profile → , *Samir N. AjaniCorresponding authorsamir.ajani@gmail.comSchool of Computer Science and EngineeringRamdeobaba University (RBU)Nagpur, Maharashtra, 440013, IndiaView full profile → , Prakhar Goyalprakhar.qsb@quantumeducation.inQuantum University Research CenterQuantum UniversityRoorkee, Uttarakhand, 247667, IndiaView full profile → , Sanjesh Sadanand Pawalesanjesh.pawale@vupune.ac.inDepartment of Computer EngineeringVishwakarma UniversityPune, Maharashtra, 411048, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Apr 2026
- Published Online:
- 31 Oct 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-3048
- Pages:
- 4249–4259
Abstract
The algebraic graph theory has a framework to study and construct secure communication systems based on a combination of structural graph properties, spectral graph properties and cryptographic concepts. This paper discusses attack modelling based on graphs with the actions of adversaries being modelled with respect to the edge between nodes, and the intrusion patterns can be formally defined. The spectral graph techniques are employed to detect anomalies that are determined by the eigenvalue distribution, laplacian matrices and connectivity to make it more accurate and robust. Further, algebraic structures, such as groups, rings and finite fields are also added to graph based cryptographic constructions to have a greater confidentiality and integrity. The proposed model is more robust in security where accuracy of intrusion detection is 28 percent better and a reduction in attack propagation is 22 percent, as compared to traditional ones. Results highlight the power, scalability and usability in dynamical network systems. The approach offers a unique, mathematical foundation of the design of secure communication, future developments of intelligent, graph driven cybersecurity systems.
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References
[1] S. A. U. H. Bokhary, A. Kharal, F. M. A. Samman, M. E. E. Dalam, and A. Gargouri, “Efficient graph algorithms in securing communication networks,” Symmetry, vol. 16, no. 10, Art. no. 1269 (2024), doi: 10.3390/sym16101269.
[2] G. Jayabalasamy, C. Pujol, and K. Latha Bhaskaran, “Application of graph theory for blockchain technologies,” Mathematics, vol. 12, no. 8, Art. no. 1133 (2024), doi: 10.3390/math12081133.
[3] Z. Wei, L. Wang, S. C. Sun, B. Li, and W. Guo, “Graph layer security: Encrypting information via common networked physics,” Sensors, vol. 22, no. 10, Art. no. 3951 (2022), doi: 10.3390/s22103951.
[4] A. Netto Mertia and M. Sudha, “Synthesis of index difference graph structures for cryptographic implementation,” Symmetry, vol. 17, no. 9, Art. no. 1568 (2025), doi: 10.3390/sym17091568.
[5] K. Griparić, “Algebraic connectivity control in distributed networks by using multiple communication channels,” Sensors, vol. 21, no. 15, Art. no. 5014 (2021), doi: 10.3390/s21155014.
[6] A. Majeed and I. Rauf, “Graph theory: A comprehensive survey about graph theory applications in computer science and social networks,” Inventions, vol. 5, no. 1, Art. no. 10 (2020), doi: 10.3390/inventions5010010.
[7] N. Almalki and P. Kaemawichanurat, “Structural properties of connected domination critical graphs,” Mathematics, vol. 9, no. 20, Art. no. 2568 (2021), doi: 10.3390/math9202568.
[8] P. Sahane, M. Gulhane, N. Rakesh, S. M. M. Naidu, M. Grover, and V. Mahajan, “Evaluating lightweight encryption schemes for resource-constrained devices in wireless sensor networks,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 28, no. 5-A, pp. 1803–1812 (2025).
[9] D. Medvedev, U. Shani, and D. Dori, “Gaining insights into conceptual models: A graph-theoretic querying approach,” Applied Sciences, vol. 11, no. 2, Art. no. 765 (2021), doi: 10.3390/app11020765.
[10] M. Zhao, H. Wang, and B. Yao, “Graphic groups, graph homomorphisms, and graphic group lattices in asymmetric topology cryptography,” Entropy, vol. 25, no. 5, Art. no. 720 (2023), doi: 10.3390/e25050720.
[11] P. J. Roig, S. Alcaraz, K. Gilly, C. Bernad, and C. Juiz, “Formal algebraic model of an edge data center with a redundant ring topology,” Network, vol. 3, no. 1, pp. 142–157 (2023), doi: 10.3390/network3010007.
[12] E. M. Visalakshidevi and N. Kalaivani, “A comparative approach for decision making models,” Journal of Information and Optimization Sciences, vol. 47, no. 4, pp. 1249–1262 (2026), doi: 10.47974/JIOS-2171.
[13] G. Tsitsiashvili, “Construction and analysis of queuing and reliability models using random graphs,” Mathematics, vol. 9, no. 19, Art. no. 2511 (2021), doi: 10.3390/math9192511.
[14] S. Madhumitha and S. Naduvath, “Graphs defined on rings: A review,” Mathematics, vol. 11, no. 17, Art. no. 3643 (2023), doi: 10.3390/math11173643.
[15] R. N. A. Prasad, “Quantum computing applications in theoretical and applied physics: A systematic review,” IJISEA Publications (2026), doi: 10.5281/zenodo.20082583.
