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.
Age 16 to 18 Challenge Level:
The use of set terminology here should not hold anyone up as they can
find the definition in the Thesaurus. This is an exercise in
combinatorics and it also gives a method for solving the problem about
the sequence of subsets.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.