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VCE 11 General 2023

8.05 Traverse connected graphs

Worksheet
Traversable networks
1

State whether the following networks are traversable:

a
b
c
d
e
f
g
h
i
j
2

For each of the networks below, state which vertices you can start at in order to traverse the network:

a
b
3

Consider the following network:

a
Determine if the network is traversable and state why.
b
Which vertices can you start at in order to traverse the network?
c
What sets apart the start and end vertices chosen in part (b) from other vertices in the network?
Applications
4

A team of workers is to repair seven bridges that cross the river running through town, as shown in the image below:

a

After repairing each bridge (which involves crossing the bridge), the workers close it off for 24 hours.

Given that they start in the bottom-left area of the town (where the truck is in the image), can the workers repair all seven bridges in one day without going back over a closed bridge?

b

After repairing all seven bridges, which road do the workers leave by: top left, bottom left, top right or bottom right?

5

A machine must print four different circuit boards connecting components A, B, C and D as shown below. State whether each circuit board can be printed without the printer lifting from the board or retracting a path. Explain your answer.

a
b
c
d
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Outcomes

U2.AoS2.5

apply the concepts of connected graphs: trails, paths, circuits, bridges and cycles to model and solve practical problems related to traversing a graph

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