Abstract
This chapter discusses graph theory where a graph G = (V, E) consists of vertices and edges. It is a practical branch of mathematics that deals with the arrangements of vertices and edges between them, and it has been applied to practical problems such as the modelling of computer networks, determining the shortest driving route between two cities, and the travelling salesman problem.
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Notes
- 1.
The four-colour theorem states that given any map it is possible to colour the regions of the map with no more than four colours such that no two adjacent regions have the same colour. This result was finally proved in the mid-1970s.
- 2.
Königsberg was founded in the thirteenth century by Teutonic knights and was one of the cities of the Hanseatic League. It was the historical capital of East Prussia (historical part of Germany), and it was annexed by Russia at the end of the Second World War. The German population either fled the advancing Red army or were expelled by the Russians in 1949. The city is now called Kaliningrad. The famous German philosopher, Immanuel Kant, spent all his life in the city and is buried there.
- 3.
These are named after Sir William Rowan Hamilton, a nineteenth-century Irish mathematician and astronomer, who is famous for discovering quaternions discussed in a later chapter.
- 4.
We use the term “salesman” to stand for “salesman” or “saleswoman”.
Reference
Piff M (1991) Discrete mathematics. An introduction for software engineers. Cambridge University Press
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O’Regan, G. (2023). Graph Theory. In: Mathematical Foundations of Software Engineering. Texts in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-26212-8_7
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DOI: https://doi.org/10.1007/978-3-031-26212-8_7
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