The+Graph+Theory

The Graph Theory

The Graph Theory, also known as the Seven Bridges of Königsberg was solved by Euler. This puzzle included a city called Königsberg, Prussia, had a river running through it forming two islands. 7 bridges surrounded the land and crossed the river on all sides of the main island.



The question was, can you cross all of the bridges only once. Euler’s approach was to mark out the points of land (there were 4) and make them the points to be visited. The paths between them (on the diagram) were the bridges. This was called the Graph Theory.

A graph is made up of points (known as a vertex or vertices) and straight or curved lines (edges) joining them. So the problem is solved by tracing over the graph and then seeing if you can only trace over each edge once. So Euler's solution was that all but two of the vertices must have an edge leading in and out of it. The two that must have one leading to and from it must be the one you start at and the one you finish at. When it is explained it is simple, but I bet you never thought about that yourself! ;)