Efficient Genome Assembly Studies Using Overlap and Hamiltonian Graphs

Abstract

These DNA sequencing is the intricate process of deciphering the specific arrangement of nitrogenous bases, also known as nucleotides, within a DNA molecule. Each organism possesses a unique nucleotide sequence that dictates its genetic blueprint, or genome, influencing both physical traits (phenotypes) and hereditary characteristics (genotypes) at the cellular level. In the realm of mathematics, graph theory delves into the study of mathematical constructs called graphs, composed of vertices (nodes) interconnected by either directed or undirected edges. Determining the precise order in which these nucleotides are linked empowers scientists and researchers to compare DNA across organisms, shedding light on their evolutionary relationships. This research delves into the pivotal role of graph theory in genome sequencing, exploring the diverse types of graphs utilized in this process. We propose innovative methods for employing graph theory in DNA sequencing and investigate the application of graphs such as overlap graphs and Hamiltonian graphs in genome sequencing, along with their associated advantages and limitations.