Knot Theory and Its Applications pp 284-298 | Cite as

# Graph Theory Applied to Chemistry

## Abstract

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 {V_{G}, E_{G}} that fulfills an *incidence relation*. An element of V_{G} is then said to be a *vertex* of G, while an element of E_{G} is said to be an *edge* of G. The relation/condition mentioned above stipulates that an element, e, of E_{G} is *incident* to elements, say, a and b, of V_{G} (*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.

## Keywords

Plane Graph Complete Graph Abstract Graph Dual Graph Orientation Preserve## Preview

Unable to display preview. Download preview PDF.