Applications of Graph Theory towards Data Storage Media

Graph theory, which studies the theoretical properties of graphs, is an area of applied and discrete mathematics, and has various applications towards engineering. For example, network topologies can be characterized by graphs and those topologies can be used to find better solutions in smooth communications. In this paper, we explain how graph theory has been applied in data storage media. In particular, we explain storing/reading schemes for typical data storage media, and then present how graph theory plays an important role in coding for data storage media, together with our contributions. More precisely, we review our results from constrained systems, which control the appearance of certain data sequences, and how the results work for reliable data storage media