Introduction to Graph Theory

Abstract

The objects that we study in the branch of mathematics known as graph theory are not graphs drawn with x and y axes. In this chapter, the word ‘graph’ refers to a structure consisting of points (called ‘vertices’), some of which may be joined to other vertices by lines (called ‘edges’) to form a network. Structures of this type abound in computing. The computers on a site may be connected into a local area network, which in turn may be linked to national and international communications networks. The circuitry inside a computer (which we represented schematically by digital circuit diagrams in Chapter 8) is another example of a graph or network structure. At a more abstract level, we saw in Chapter 5 how a relation on a set can be depicted using a diagram that takes the form of a graph.