Networks/graph theory

Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.

Explore some of the different types of network, and prove a result about network trees.

Explore creating 'factors and multiples' graphs such that no lines joining the numbers cross

Look for the common features in these graphs. Which graphs belong together?

Think about the mathematics of round robin scheduling.

The graph represents a salesman’s area of activity with the shops that the salesman must visit each day. What route around the shops has the minimum total distance?

Without taking your pencil off the paper or going over a line or passing through one of the points twice, can you follow each of the networks?

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry

Prove that you cannot form a Magic W with a total of 12 or less or with a with a total of 18 or more.

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?