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ABSTRACT
This study aims to present a detailed investigation of the properties and characteristics of Eulerian graphs. Eulerian graphs are a special class of graphs that have a cycle traversing all edges exactly once. To explore the fundamental properties of Eulerian graphs, various graph theoretical concepts and techniques have to be employed. This project examines the degree sequences, connectivity, and planarity of Eulerian graphs. In addition, this study investigates different algorithms used for finding Eulerian paths and circuits in graphs, including Hierholzer’s algorithm and Fleury’s algorithm and Dijkstra’s algorithm for finding the shortest path in routing problems. The results of this project provides a deeper understanding of Eulerian graphs and their application in computer science, network analysis, DNA sequencing and engineering. The findings can contribute to the development of algorithms and techniques for solving problems in diverse fields such as transportation networks, computer networks, DNA sequencing, and Scheduling problems.
