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The increasingly complex growth of urban mobility requires an analytical approach that can optimize transportation networks effectively and sustainably. Graph theory is one of the mathematical methods widely used in modeling road network structures and analyzing inter-node connectivity to obtain more efficient routing and network optimization solutions. This study aims to systematically review the development of graph theory application in urban transportation network optimization through the Systematic Literature Review (SLR) method. The review was conducted following the PRISMA 2020 protocol for articles published between 2020 and 2025. A total of ten articles met the inclusion criteria and were analyzed in depth. The review results show that graph algorithms such as Dijkstra, Bellman–Ford, Floyd–Warshall, Minimum Spanning Tree (MST), Graph Neural Network (GNN), and the hybrid Dijkstra–A* method can improve route efficiency, reduce travel time, improve navigation accuracy, and strengthen congestion prediction capabilities. In general, graph theory has proven to be an effective and adaptive approach in supporting urban transportation network planning and management. Further research is recommended to integrate graph theory with real-time traffic data and artificial intelligence technology to improve the accuracy and responsiveness of modern transportation systems.

This study aims to examine the application of the Hungarian method in solving assignment problems based on linear programming, particularly in optimizing work time allocation. Through a literature review of 15 research articles, it was found that the Hungarian method consistently proves effective in improving work efficiency, reducing time waste, and optimally matching resources with appropriate tasks. These studies reported reductions in work time ranging from 3 to 663 minutes after applying the method, depending on the complexity and context of each case. Additionally, integrating the Hungarian method with software tools such as POM-QM and LINGO further accelerates the optimization process. The findings indicate that the Hungarian method is a practical, flexible, and relevant mathematical approach across various sectors, supporting operational decision-making in an objective and efficient manner.

This study aims to analyze the derivatives of a two-variable function and visualize the results in the form of a 3D graph using Python. Derivatives of two-variable functions are essential in multivariate analysis, such as optimization and surface analysis. The study uses Visual Studio Code as the Integrated Development Environment (IDE) to develop and run Python code, utilizing libraries such as NumPy, SymPy, and Matplotlib for mathematical computations and visualization. The first step involves programming partial derivatives of a two-variable function using SymPy. Subsequently, the derivative results are visualized in 3D using Matplotlib to illustrate the surface and gradient of the function. The goal of this research is to provide a deeper understanding of the application of derivatives in two-variable functions and the benefits of visualization in analyzing these derivative results. The findings are expected to contribute to the fields of mathematics education and numerical computation applications.