Graph - Theoretic Optimization of Transportation Networks Using Shortest-Path Algorithms

Graph theory is an important branch of discrete mathematics that provides mathematical models for representing and analyzing interconnected systems.Transportation networks can naturally be represented as weighted graphs, where locations are modeled as vertices, roads as edges, and distance, travel time, or transportation cost as edge weights.This research investigates the application of graph-theoretic methods for optimizing routes in transportation networks.A mathematical graph model is developed to represent connections between different locations, and shortestpath algorithms, particularly Dijkstra's algorithm, are applied to identify efficient routes between selected source and destination vertices.Different route conditions can be analyzed by modifying edge weights or considering changes in network connectivity.The study evaluates the effectiveness of graph-based shortest-path optimization in minimizing travel distance or cost and demonstrates how mathematical graph models can support practical transportation decision-making.The proposed approach provides a foundation for extending graph-based optimization to dynamic transportation networks, real-time traffic conditions, and intelligent route-planning systems.