This abstract delves into the intricate intersection of Graph Theory and Genetics, focusing on the pivotal role of Eulerian and De Bruijn graphs in deciphering the complexities of genome assembly. Genome assembly, a fundamental challenge in bioinformatics, involves reconstructing the complete DNA sequence of an organism from short, fragmented reads. By leveraging graph theory concepts, specifically Eulerian and De Bruijn graphs, researchers can navigate through this intricate puzzle of genetic information. Eulerian graphs, pioneered by Leonhard Euler in the 18th century, provide a powerful framework for analyzing interconnected paths within genomic data. These graphs offer a systematic approach to trace the sequence of DNA fragments and identify overlaps, crucial for reconstructing the entire genome accurately. On the other hand, De Bruijn graphs, named after mathematician Nicolaas Govert de Bruijn, offer a more efficient representation of genomic sequences by breaking them into smaller, overlapping k-mers. This abstract explores how these graph structures serve as indispensable tools in genome assembly by enabling researchers to address challenges such as repetitive sequences, sequencing errors, and genome complexity. By dissecting genetic information into manageable components and reconstructing the original sequence through graph traversal algorithms, scientists can unravel the mysteries encoded within the DNA strands. This exploration not only enhances our theoretical understanding of graph-based genome assembly but also provides valuable insights into the practical considerations and applications of Eulerian and De Bruijn Graphs in the ever-evolving landscape of genomics