Graph Theory

A graph is conceptually a set of points and a set of lines joining one point to another. Graph theory has its origins in many disciplines. Graphs are natural mathematical models of physical situations in which the points represent either objects or locations and the lines represent connections. Graphs are also used to model sociological and abstract situations in which each line represents a relationship between the entities represented by the points. This chapter contains an extensive treatment of the various properties of graphs. Due to the vast breadth of the usefulness of graphs, the terminology varies widely, not only from one type of graph to another, but also from one application to another. To apply a computer to graph-theoretic computations, it is necessary to specify the underlying graph completely and without ambiguity. The representations are also useful in their own right.