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 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 | ||
| 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 | ||
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