The study of mathematics is important in many fields. One of the key areas of mathematics used in structural models is graph theory. This organizational structure of various items or technologies encourages new discoveries and modifications to the state of the art in these fields. The Koinsberg Bridge problem marked the beginning of the field graph theory in 1735. This article describes the usage of graphical theory in a variety of diverse fields, however it mostly focuses on information science, electrical engineering, linguistics, physics, chemistry, computer network science, biotechnology, and applications of graphical theory. In order to understand scheduling concepts, engineering technology implementations, and an overview, several publications on graph theory have been reviewed.