Networks/graph theory

problem
Only connect

Age

11 to 14

Challenge level

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?
problem
Classifying solids using angle deficiency

Age

11 to 16

Challenge level

Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
problem
Magic W wrap up

Age

16 to 18

Challenge level

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.
problem
Travelling salesman

Age

11 to 14

Challenge level

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?
problem
The bridges of Konigsberg

Age

11 to 18

Challenge level

Investigate how networks can be used to solve a problem for the 18th Century inhabitants of Konigsberg.
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.
problem
Round-robin scheduling

Age

7 to 14

Challenge level

Think about the mathematics of round robin scheduling.
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
problem
Network trees

Age

14 to 18

Challenge level

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

Age

14 to 16

Challenge level

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.