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Published in:
What Is a Computer? Read chapter Read first chapter

2020 | OriginalPaper | Chapter

9. Graph Theory

Author : Gerard O’Regan

Published in: Mathematics in Computing

Publisher: Springer International Publishing

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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 arrangement 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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previous chapter Mathematical Induction and Recursion
next chapter Cryptography
Footnotes
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 (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 Chap. 26.
 
4
We use the term ‘salesman’ to stand for ‘salesman’ or ‘saleswoman’.
 
Literature
Piff M (1991) Discrete mathematics: an introduction for software engineers. Cambridge University Press
Metadata
Title
Graph Theory
Author
Gerard O’Regan
Copyright Year
2020
Book
Mathematics in Computing

Print ISBN: 978-3-030-34208-1

Electronic ISBN: 978-3-030-34209-8

Copyright Year: 2020

DOI
https://doi.org/10.1007/978-3-030-34209-8_9

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