Mathigon
Mathigon: Graphs and Networks: Graphs in Everyday Life
This lesson focuses on graphs in everyday life including virtual graphs such as the Internet or physical computer networks of computers. It puts graph theory into practice and provides examples and learning exercises.
Mathigon
Mathigon: Graphs and Networks: Map Colouring
This lesson focuses on map coloring and the problem of proving that 4 colors would work for all maps. Francis Guthrie had to color a map of counties in England. He observed that four colors seemed to suffice for any map he tried, but he...
Mathigon
Mathigon: Graphs and Networks: The Bridges of Konigsberg
This lesson focuses on developing a way to cross all 7 Bridges of Konigsberg without crossing any of them more than once. Euler discovered it was impossible, but he developed the idea of using graph theory to determine if it would be...
Mathigon
Mathigon: Graphs and Networks: Parties and Dating
This lesson uses handshakes at a party to explain complete graphs, when every vertex is connected to every other vertex. It shows how a formula was created to calculate the number of edges.
Mathigon
Mathigon: Graphs and Networks: The Travelling Salesman Problem
This lesson focuses on the traveling salesman problem which involves finding paths through a city without backtracking. While no algorithm has been found to do that for all cities, there are algorithms that help somewhat. They are...
Mathigon
Mathigon: Graphs and Networks: Planar Graphs
Here is another puzzle that is related to graph theory. In a small village there are three utility plants producing water, electricity and gas respectively. There are also three houses which need to be served. Unfortunately, due to the...
Mathigon
Mathigon: Graphs and Networks: Euler's Formula
This lesson focuses on Euler's Equation. Any (finite) graph can be constructed by starting with one vertex and adding more vertices one by one. We have shown that, whichever way we add new vertices, Euler's equation is valid. Therefore...