Graph Theory Applied to Chemistry

In our discussions thus far we have considered a graph to be a figure, to put it naively, composed of dots and line segments (topologically this is called a 1-complex). To be more exact, less intuitive, and more mathematical, a graph is usually thought of in an abstract sense. Therefore, strictly speaking, a (finite) graph G is a pair of (finite) sets {VG, EG} that fulfills an incidence relation. An element of VG is then said to be a vertex of G, while an element of EG is said to be an edge of G. The relation/condition mentioned above stipulates that an element, e, of EG is incident to elements, say, a and b, of VG (nota bene, the condition does not require a and b to be distinct.) The two vertices a and b are said to be endpoints of e. If it is the case that a = b, then e is said to be a loop.