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.

Label this plum tree graph to make it totally magic!

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

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?

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?

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

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

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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?