Discrete Mathematics for IT: Euler Circuit and Its Applications

This report provides a comprehensive investigation into Euler circuits, a fundamental concept in discrete mathematics and graph theory. It begins with a clear problem definition, explaining the difference between Euler paths and circuits and providing illustrative examples. The report then explores the real-world applications of Euler circuits, including their use in optimizing routes for mail delivery, paving roads, and solving the Konigsberg bridge problem and travelling salesman problems. The report details the criteria for constructing Euler circuits, including the requirement that all vertices in the graph must have an even degree. The report also describes the Eulerisation process, used to transform graphs into Eulerian graphs by duplicating edges. Furthermore, the report outlines Fleury's algorithm, a key method for constructing Euler circuits. The report concludes by highlighting the practical benefits of understanding and applying Euler circuits for solving real-world problems and optimizing various business operations. This is a student assignment and is available on Desklib, a platform offering AI-based study tools.