Graph Theory: Its Importance and Application in Recent development of Science and Engineering

Abstract

Graph Theory is widely used in all the basic sciences including social science, due to its intrinsic simplicity it has got a lot of application in computer science, computer networks, engineering, genetics, data structure etc. Graphs are nothing but mathematical structure that helps in representing our everyday problem in a precise graphical manner. Graph Theory is the area of applied mathematics that deals with the study of objects and the relationship about them. The issue of finding the shortest path is extensively researched within network flow optimization problems. It holds significant relevance in multiple scientific and engineering domains, particularly in areas like transportation and traffic control, where solving various types of shortest path problems becomes essential. The transportation scientist requires a very flexible and efficient shortest path methods and applications, to solve the real world problem both from the time point of view, and also for the memory requirements applied for the same. Also, graph theoretical reasoning can cast light on such problems, providing tools which help in making decisions and help in finding answers to a variety of specific problems or questions which arises in the attempt to tackle the broader issues. Every real world problem can be converted into a mathematical problem and can be solved with the help of graph theory. Due to its intrinsic nature, graph theory is one of the important tool to study various mathematical structures and to analysis its insights.