Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree has exactly one more vertex than it has edges.
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
A graph is a set of vertices (or nodes), together with a set of edges (or arcs).
Look at the graphs below. You can print them off as a set of cards here.
Can you find graphs that you think 'belong' together in some sense?
Can you describe the features they have in common?
Could you draw more graphs that 'belong' in the same set?
Click below to see some definitions used to describe graphs.
Can you find examples on the cards that match each definition? Can you draw some more examples of your own?