1. Structures 7 Decision Maths: Graph Theory, Networks and Algorithms

2. Königsberg Bridge Problem Is it possible to walk around the town, crossing every bridge exactly once?

3. Generalising the Königsberg Bridge problem: How can you decide whether a given graph is traversable or not? Where should you start tracing?

4. Euler’s relation for planar graphs v = number of vertices e = number of edges f = number of faces (including the ‘infinite’ face) v – e + f = 2 XX X

5. and Euler’s relation for solids

6. what about …?

7. Network problems and algorithms minimum connector problem minimum length of cable required to connect all towns shortest path shortest route between two towns travelling salesman minimum distance needed to visit all towns Chinese postman minimum distance to travel along every road