A traversable graph is one you can draw without taking your pen off the paper, and without going over any edge twice.
For each graph below, decide whether or not it it traversable. It might be helpful to keep a track of where you started, the route you took, and where you finished.
What do you notice about traversable graphs where you started and finished in the same place?
What about traversable graphs where you started and finished in different places?
What do you notice about the number of times you visited each node?
Can you find a condition that guarantees a graph is not traversable?
Can you explain why?
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.