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Eshaghi, Madjid, Jabbari, Ali. (1404). On the algebraic and topological structure of temporal graphs: A unified framework for $(f, g)$-homomorphisms and Spatio-Temporal flows. نشریه هنرهای کاربردی, (), -. doi: 10.22075/ijnaa.2025.10333
Madjid Eshaghi; Ali Jabbari. "On the algebraic and topological structure of temporal graphs: A unified framework for $(f, g)$-homomorphisms and Spatio-Temporal flows". نشریه هنرهای کاربردی, , , 1404, -. doi: 10.22075/ijnaa.2025.10333
Eshaghi, Madjid, Jabbari, Ali. (1404). 'On the algebraic and topological structure of temporal graphs: A unified framework for $(f, g)$-homomorphisms and Spatio-Temporal flows', نشریه هنرهای کاربردی, (), pp. -. doi: 10.22075/ijnaa.2025.10333
Eshaghi, Madjid, Jabbari, Ali. On the algebraic and topological structure of temporal graphs: A unified framework for $(f, g)$-homomorphisms and Spatio-Temporal flows. نشریه هنرهای کاربردی, 1404; (): -. doi: 10.22075/ijnaa.2025.10333

On the algebraic and topological structure of temporal graphs: A unified framework for $(f, g)$-homomorphisms and Spatio-Temporal flows

International Journal of Nonlinear Analysis and Applications
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 21 آذر 1404    اصل مقاله (548.77 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2025.10333
نویسندگان
Madjid Eshaghi* 1؛ Ali Jabbari2
1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran
2Applied Mathematics and Informatics, Kyrgyz-Turkish Manas University, Bishkek, Kyrgyzstan
تاریخ دریافت: 14 خرداد 1404،  تاریخ بازنگری: 15 مرداد 1404،  تاریخ پذیرش: 06 آبان 1404 
چکیده
Modelling complex systems where connections are transient requires a departure from static graph theory. This paper proposes a comprehensive mathematical framework for {Temporal Graphs}, extending classical concepts to capture dynamic interactions and causality. We identify fundamental limitations in static representations, specifically the "Path Existence Fallacy" and "Flow Indistinguishability." To resolve these, we introduce the novel concept of {$(f, g)$-homomorphism}, a structural mapping $f$ coupled with a temporal mapping $g$, which allows for the modelling of time dilation, contraction, and reversal within network flows. Furthermore, we define hierarchical temporal graphs (HTGs) for multi-scale analysis. Finally, we present a rigorous list of open problems in pure mathematics—ranging from temporal fixed point theory to persistent homology—and future applications in quantum computing and blockchain dynamics.
کلیدواژه‌ها
Temporal Graphs؛ (f,g)-Homomorphism؛ Dynamic Networks؛ Time-Varying Topology؛ Causal Paths؛ Fixed Point Theory
مراجع

[1] F. Harary and G. Gupta, Dynamic graph models, Math. Comput. Modell. 25 (1997), no. 7, 79–87.

[2] D. Kempe, J. Kleinberg, and A. Kumar, Connectivity and inference problems for temporal networks, J. Comput. Syst. Sci. 64 (2002), no. 4, 820–842.

[3] P. Holme and J. Saramaki, Temporal networks, Phys. Rep. 519 (2012), no. 3, 97–125.

[4] N. Masuda and R. Lambiotte, A Guide to Temporal Networks, World Scientific, 2016.

[5] O. Michail, Introduction to temporal graphs: An algorithmic perspective, Internet Math. 12 (2016), no. 4, 239–280.

[6] A. Casteigts, P. Flocchini, W. Quattrociocchi, and N. Santoro, Time-varying graphs and dynamic networks, Int. J. Parallel Emergent Distrib. Syst. 27 (2012), no. 5, 387–408.

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