For the following graph, identify whether the graph is traversable, or not. For the traversable graphs, identify a trail which traverses the network.

For the following graph, identify whether the graph is traversable, or not. For the traversable graphs, identify a trail which traverses the network.

For the following graph, identify whether the graph is traversable, or not. For the traversable graphs, identify a trail which traverses the network.

For the following graph, identify whether the graph is traversable, or not. For the traversable graphs, identify a trail which traverses the network.

For the following graph, identify whether the graph is traversable, or not. For the traversable graphs, identify a trail which traverses the network.

For the following graph, identify whether the graph is traversable, or not. For the traversable graphs, identify a trail which traverses the network.

A team of workers are repainting the central lines on a series of roads. The painting machine moves slowly (whether or not it is painting) so they wish to find the shortest route possible which takes in all of the roads, and then return to their start point so it can be loaded back onto their truck. This network shows the configuration of the roads and the weights are the times (in minutes) taken to travel down the road. They park at $A$.
By determining which roads they should travel down twice, find the minimum time needed for them to complete the task and the routes they need to duplicate. Suggest a possible route that they could take.

As part of her daily exercise regime, a pensioner decides that she will walk along every path in her local park. The paths and the times (in minutes) taken to walk along them are illustrated below. Her walk starts at the gate at $A$.

Explain why the route $AB$ must be doubled.

As part of her daily exercise regime, a pensioner decides that she will walk along every path in her local park. The paths and the times (in minutes) taken to walk along them are illustrated below. Her walk starts at the gate at $A$.

Explain why the route $AB$ must be doubled.

Identify which other routes should be doubled so that her walk is as short as possible.