Linear and Circular Models of Graphs

The fundamental common concept of all applied mathematics is a mathematical model. Before the twentieth century, most of mathematics, pure and applied, was concerned with the analysis of mathematical models of physical phenomena. Since the advent of digital computers, problems involving discrete mathematical models have become increasingly important. Computer science and operations research deal with complex structures having discrete (or finitely described) relationships as opposed to the continuous relationships embodied in the laws of physics. This article uses a basic discrete mathematical model, called a graph, to illustrate the point that modeling is a two-way street . That is, mathematical problems are often clarified by use of a physical model that can provide a physical picture and new insight into the mathematics.