Introduction to quantum graphs and their stability analysis

Samanta, Sovan; Allahviranloo, Tofigh

doi:10.22034/cmde.2025.63178.2816

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	Introduction to quantum graphs and their stability analysis
Computational Methods for Differential Equations
مقاله 3، دوره 14، شماره 3، مهر 2026، صفحه 1025-1039 اصل مقاله (964.55 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.63178.2816
نویسندگان
Sovan Samanta^* ¹؛ Tofigh Allahviranloo²
¹1. Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, W.B-721636, India. 2. Research Center of Performance and Productivity Analysis, Istinye University, Istanbul, Türkiye.
²1. Research Center of Performance and Productivity Analysis, Istinye University, Istanbul, Türkiye. 2. Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
چکیده
Quantum graphs have dynamic vertices and edges. The vertices and edges are assigned by functions. These types of representations of graphs can represent time-dependent network structures. The network characteristics can be visible at any point in time. The networks, such as brain networks or biological disease networks, can be represented by quantum graphs, and hence the characteristics and parameters of quantum graphs are an important research area. This study discusses the properties of quantum graphs. Additionally, real examples and the area of applications are provided.
کلیدواژه‌ها
Quantum Graphs؛ Dynamical Systems؛ Quantum Networks؛ Stability Analysis

مراجع
[1] A. A. Adeniji, M. O. Adeniyi, and M. Y. Shatalov, Mathematical model and stability analysis of university-PhD- postdoc-industry migration and unemployment in South Africa, J. Math. Comput. Sci., 31(1) (2023), 81-94. [2] T. Allahviranloo, A. Jafarian, R. Saneifard, N. Ghalami, S. Measoomy Nia, F. Kiani, and S. Noeiaghdam, An application of artificial neural networks for solving fractional higher-order linear integro-differential equations, Boundary Value Problems, 2023(1) (2023), 74. [3] T. Allahviranloo and S. Samanta, Quantum Theory and Fuzzy Systems: Traversing Uncertainty in Group Decision-Making and Social Networks, e-ISBN: 978-3-031-82058-8, Studies in Computational Intelligence, Springer, 2025, e-ISSN:1860-9503. [4] D. S. Bassett and E. D. Bullmore, Small-world brain networks, The Neuroscientist, 12(6) (2006), 512-523. [5] C. H. Bennett and G. Brassard, An update on quantum cryptography, In Workshop on the theory and application of cryptographic techniques, Berlin, Heidelberg: Springer Berlin Heidelberg, (1984, August), 475-480. [6] M. Brang, H. Franke, F. Greinert, M. S. Ubben, F. Hennig, and P. Bitzenbauer, Spooky action at a distance? A two-phase study into learners’ views of quantum entanglement, EPJ Quantum Technology, 11(1) (2024), 33. [7] E. Bullmore and O. Sporns, Complex brain networks: graph theoretical analysis of structural and functional systems, Nature Reviews Neuroscience, 10(3) (2009), 186-198. [8] S. L. Cornish, M. R. Tarbutt, and K. R. Hazzard, Quantum computation and quantum simulation with ultracold molecules, Nature Physics, (2024), 1-11. [9] K. Das, A. Maity, K. De, S. Mondal, S. Samanta, and T. Allahviranloo, Link Prediction in Co-Authorship Network Under Fuzziness and Application in Biomedical Analysis, Fuzzy Information and Engineering, 16(2) (2024), 155- 174. [10] J. F. Dynes, A. Wonfor, W. S. Tam, A. W. Sharpe, R. Takahashi, M. Lucamarini, and et al., Cambridge quantum network, npj Quantum Information, 5(1) (2019), 101. [11] Z. Eidinejad, R. Saadati, and T. Allahviranloo, Attractiveness of pseudo almost periodic solutions for delayed cellular neural networks in the context of fuzzy measure theory in matrix-valued fuzzy spaces, Computational and Applied Mathematics, 41(8) (2022), 369. [12] A. H. Ghaderi, B. R. Baltaretu, M. N. Andevari, V. Bharmauria, and F. Balci, Synchrony and complexity in state-related EEG networks: an application of spectral graph theory, Neural Computation, 32(12) (2020), 2422- 2454. [13] Z. Ghasemi, M. Afshar Kermani, and T. Allahviranloo, Developing an Intelligent Model Based on Fuzzy Multilayer Neural Network for Improving Credit Risk Management under Uncertain Conditions, Mathematical Problems in Engineering, 2023(1) (2023), 4141140. [14] D. Ghosh, M. Frasca, A. Rizzo, S. Majhi, S. Rakshit, K. Alfaro-Bittner, and S. Boccaletti, The synchronized dynamics of time-varying networks, Physics Reports, 949 (2022), 1-63. [15] F. Hosseinzadeh Lotfi, T. Allahviranloo, W. Pedrycz, M. R. Mozaffari, and J. Gerami, The Two-Stage Net- work Based on Ratio Analysis Models, In Comparative Efficiency in Data Envelopment Analysis Based on Ratio Analysis, Cham: Springer International Publishing, (2023), 139-155. [16] M. Jayapriya, A. Ganesh, S. S. Santra, R. Edwan, D. Baleanu, and K. M. Khedher, Sawi transform and Hyers- Ulam stability of nth order linear differential equations, 28(4) (2022), 393–411. [17] T. Kottos and U. Smilansky, Quantum chaos on graphs, Physical Review Letters, 79(24) (1997), 4794. [18] S. Lloyd, Universal quantum simulators, Science, 273(5278) (1996), 1073-1078. [19] P. Mandal, S. Samanta, M. Pal, and A. S. C. Ranadive, Social network trust relationship environment based advanced ovarian cancer treatment decision-making model: An approach based on linguistic information with experts’ multiple confidence levels, Expert Systems with Applications, 229 (2023), 120407. [20] A. Skolik, M. Cattelan, S. Yarkoni, T. Bäck, and V. Dunjko, Equivariant quantum circuits for learning on weighted graphs, npj Quantum Information, 9(1) (2023), 47. [21] R. Murali, A. P. Selvan, and S. Baskaran, Stability of linear differential equation of higher order using Mahgoub transforms, J. Math. Comput. Sci., 30 (2023), 1-9. [22] A. L. Olutimo, A. Bilesanmi, and I. D. Omoko, Stability and boundedness analysis for a system of two nonlinear delay differential equations, J. Nonlinear Sci. Appl., 16(2) (2023), 90-98. [23] S. Perseguers, M. Lewenstein, A. Acin, and J. I. Cirac, Quantum random networks, Nature Physics, 6(7) (2010), 539-543. [24] F. Razavinia and G. Haghighatdoost, A route to quantum computing through the theory of quantum graphs, arXiv preprint arXiv:2404.13773. [25] S. Samanta and B. Sarkar, A study on generalized fuzzy graphs, Journal of Intelligent and Fuzzy Systems, 35(3) (2018), 3405-3412. [26] S. Samanta, G. Muhiuddin, A. M. Alanazi, and K. Das, A mathematical approach on representation of competitions: competition cluster hypergraphs, Mathematical Problems in Engineering, 2020(1) (2020), 2517415. [27] S. Samanta, M. Pal, R. Mahapatra, K. Das, and R. S. Bhadoria, A study on semi-directed graphs for social media networks, International Journal of Computational Intelligence Systems, 14(1) (2021), 1034-1041. [28] B. Sarkar and S. Samanta, Generalized fuzzy trees, International Journal of Computational Intelligence Systems,10(1) (2017), 711-420. [29] E. Schrödinger, The present situation in quantum mechanics: A translation of Schrödinger’s “Cat Paradox” paper, Quantum theory and measurement, Princeton University Press, Princeton, New Jersey, (1983), 152-167. [30] G. D. Scholes, Quantum-like states on complex synchronized networks, Proceedings of the Royal Society A, 480(2295) (2024), 20240209. [31] Y. Tang, J. Yan, and H. Edwin, From quantum graph computing to quantum graph learning: A survey, arXiv preprint arXiv:2202.09506, (2022).
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Introduction to quantum graphs and their stability analysis