Networks/graph theory

  • Tourism
    problem
    Favourite

    Tourism

    Age
    11 to 16
    Challenge level

    If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

  • Limiting Probabilities
    problem
    Favourite

    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.

  • Plum Tree
    problem

    Plum Tree

    Age
    14 to 18
    Challenge level
    Label this plum tree graph to make it totally magic!
  • W Mates
    problem

    W Mates

    Age
    16 to 18
    Challenge level
    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.
  • Only connect
    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?
  • Travelling Salesman
    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?
  • Maximum Flow
    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.
  • Factors and multiples graphs
    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
  • Magic Caterpillars
    problem

    Magic Caterpillars

    Age
    14 to 18
    Challenge level
    Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
  • Networks and Nodes
    problem

    Networks and Nodes

    Age
    7 to 11
    Challenge level
    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?
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