**Authors:** Francesca Iezzi, Ana McKellar, Lukas Cerny, Benedetta Mussati and Patrick Kinnear, with the Maths Outreach Team at The University of Edinburgh (this resource can also be found here)

These resources is a set of games, puzzles and worksheets which provide a basic introduction to the mathematical topic of graph theory, which has many real-life applications but isn’t often covered in maths in school. Graph theory has real-life applications to the maths of maps and network diagrams.

**Rivers and Bridges:** a set of problems based on the famous ‘Seven Bridges of Königsberg’ problem. *Can you find a way to walk over all the bridges in the city without travelling over the same bridge twice?*

**Guide for Teachers**- Activity 1:
**Rivers-and-Bridges—Konigsberg-Kalingrad** - Activity 2:
**Rivers-and-Bridges—Lubeck** - Activity 3:
**Rivers-and-Bridges—Matching-activity** - Activity 4:
**Rivers-and-Bridges—Budapest** - Activity 5:
**Rivers-and-Bridges—Gdansk**

**Shannon Switching game:** a game for two players. *Play the game a few times, and then the key question is: can you find a strategy that can guarantee you will win? Is there a winning strategy for the games?*

- Guide for Teachers
- Start by watching this: PowerPoint explaining the game and a written version of the PowerPoint. This presentation explains what a graph is, and explains the rules of the game
- There are also video explanations available at this link

**Join and cut**Games: see this link for the first ten versions of the games. There are also video demonstrations of how to play the games.- Games:
**virus game.**Can you stop the virus?- Shannon-Switching—Virus-game-(4×3) – slightly easier
- Shannon-Switching—Virus-game-(7×4) – slightly more complicated
- Shannon-Switching—Design-a-graph-to-win

**Transport network**games

**Graph vertex colouring:** *can you colour each dot (vertex) on the graph so that no dot is connected to another dot of the same colour? What is the smallest number of colours you can use?*