Networks/graph theory

problem
Network trees

Age

14 to 18

Challenge level

Explore some of the different types of network, and prove a result about network trees.
article
A curious collection of bridges

Read about the problem that tickled Euler's curiosity and led to a new branch of mathematics!
problem
Factors and multiples graphs

Age

16 to 18

Challenge level

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

Find out some of the mathematics behind neural networks.
problem
Simply graphs

Age

16 to 18

Challenge level

Look for the common features in these graphs. Which graphs belong together?
problem
Round-robin scheduling

Age

7 to 14

Challenge level

Think about the mathematics of round robin scheduling.
problem
The Olympic torch tour

Age

14 to 16

Challenge level

Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?
problem
Torus patterns

Age

16 to 18

Challenge level

How many different colours would be needed to colour these different patterns on a torus?
problem
Limiting probabilities

Age

16 to 18

Challenge level

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.
problem
Maximum flow

Age

16 to 18

Challenge level

Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.