50 Mathematical Concepts For Better Programming (Part 8)

Photo by Joel Filipe on Unsplash

27. Euler’s Theorem & Graph Theory

The Graph theory originated in the 18th century with an interesting story.

Königsberg was a city in historic Prussia (modern-day Russia) with 7 bridges that crossed river Pregel.

The map of Königsberg (Image from Wikipedia)

It was asked:

Is it possible to walk around Königsberg crossing each bridge exactly once?

Note that it did not matter that we finished exactly where we started.

We will come back to this after learning a few terminologies.

Graph

A Graph is a mathematical structure that consists of:

• vertices (also called nodes or points) (V) which are connected by
• edges (also called links or lines) (E)

It is represented as:

G = (V, E)

Degree

The number of edges of a particular vertex is called its Degree.