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Networks, GEN2 2024 VCAA 13

A supermarket has five departments, with areas allocated as shown on the floorplan below.
 

The floorplan is represented by the graph below.

On this graph, vertices represent departments and edges represent boundaries between two departments.

This graph is incomplete.
 

  1. Draw the missing vertex and missing edges on the graph above. Include a label.   (1 mark)

Karla is standing in the Promotional department.

She wants to visit each department in the supermarket once only.

  1.  i.  In which department will she finish?  (1 mark)
  2. ii.  What is the mathematical name for this type of journey?  (1 mark)
  3. The supermarket adds a new Entertainment department , and the floorplan is rearranged.
  4. The boundaries between the departments are represented in the adjacency matrix below, where a ' 1 ' indicates a boundary between the departments.

  1. Use the adjacency matrix to complete the floorplan below by labelling each department. The Bakery is already labelled.  (1 mark)

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a. 

 
b.i.   

b.ii. 
 

c.

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a. 

b.i. 

b.ii.

c.

Networks, GEN1 2022 VCAA 2 MC

The map below shows seven countries within Central America.
 

A network diagram was drawn with seven vertices to represent each of the countries on the map of Central America. Edges were drawn to represent a border shared between two countries.

The number of edges that this network has is

  1. 5
  2. 6
  3. 7
  4. 8
  5. 9
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There are 7 edges.


♦ Mean mark 49%.

NETWORKS, FUR2 2021 VCAA 1

Maggie's house has five rooms, and , and eight doors.

The floor plan of these rooms and doors is shown below. The outside area, , is shown shaded on the floor plan.
 

The floor plan is represented by the graph below.

On this graph, vertices represent the rooms and the outside area. Edges represent direct access to the rooms through the doors.

One edge is missing from the graph.
 

  1. On the graph above, draw the missing edge.   (1 mark)

  2. What is the degree of vertex ?   (1 mark)

  3. Maggie hires a cleaner to clean the house.
  4. It is possible for the cleaner to enter the house from the outside area, , and walk through each room only once, cleaning each room as he goes and finishing in the outside area, .
  5.  i. Complete the following to show one possible route that the cleaner could take.   (1 mark)

        
         
    ii. What is the mathematical term for such a journey?   (1 mark)

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  1.  
  3.  i.
  4. ii.
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a.

b. 
 

c.i. 

c.ii. 

NETWORKS, FUR2 2016 VCAA 1

A map of the roads connecting five suburbs of a city, Alooma (), Beachton (), Campville (), Dovenest () and Easyside (), is shown below.
 


  

  1. Starting at Beachton, which two suburbs can be driven to using only one road?   (1 mark)

A graph that represents the map of the roads is shown below.
 


 

One of the edges that connects to vertex is missing from the graph.

  1.  i. Add the missing edge to the graph above.   (1 mark)

    (Answer on the graph above)
  2. ii. Explain what the loop at represents in terms of a driver who is departing from Dovenest.   (1 mark)

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a.   

b.i. 

b.ii.

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a.  

 

b.i.   

 

b.ii. 

♦♦ Mean mark 30%.

NETWORKS, FUR1 2010 VCAA 4 MC

A board game consists of nine labelled squares as shown.

A player must start at square  and, moving one square at a time, aim to finish at square .

Each move may only be to the right one square or down one square.

A player who lands on square must stay there and cannot move again.

A player can only stop moving when they reach or .
 

vcaa-networks-fur1-2010-4
 

A digraph that shows all the possible moves that a player could make to reach  or from is

vcaa-networks-fur1-2010-4ai

vcaa-networks-fur1-2010-4aii

vcaa-networks-fur1-2010-4aiii

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NETWORKS, FUR1 2011 VCAA 3-4 MC

The map of Australia shows the six states, the Northern Territory and the Australian Capital Territory (ACT).
 

In the network diagram below, each of the vertices to represents one of the states or territories shown on the map of Australia. The edges represent a border shared between two states or between a state and a territory.
 

 
Part 1

In the network diagram, the order of the vertex that represents the Australian Capital Territory (ACT) is

A.   

B.   

C.   

D.   

E.   

 

Part 2

In the network diagram, Queensland is represented by

A.   vertex A.

B.   vertex B.

C.   vertex C.

D.   vertex D.

E.   vertex E.

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NETWORKS, FUR1 2015 VCAA 6 MC

The map below shows all road connections between five towns, , , , and .
 

NETWORKS, FUR1 2015 VCAA 6 MC1

 
A graph, shown below, was constructed to represent this map.


NETWORKS, FUR1 2015 VCAA 6 MC2

 
A mistake has been made in constructing this graph.

This mistake can be corrected by

A.   drawing another edge between and .

B.   drawing a loop at .

C.   removing the loop at .

D.   removing one edge between and .

E.   removing one edge between and .

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NETWORKS, FUR2 2008 VCAA 2

Four children, James, Dante, Tahlia and Chanel each live in a different town. 

The following is a map of the roads that link the four towns, , , and .
 

NETWORKS, FUR2 2008 VCAA 21
 

  1. How many different ways may a vehicle travel from town to town without travelling along any road more than once?   (1 mark)

James’ father has begun to draw a network diagram that represents all the routes between the four towns on the map. This is shown below.


NETWORKS, FUR2 2008 VCAA 22
 

In this network, vertices represent towns and edges represent routes between tow

  1. i. One more edge needs to be added to complete this network. Draw in this edge clearly on the diagram above.   (1 mark)

  2. ii. With reference to the network diagram, explain why a motorist at could not drive each of these routes once only and arrive back at .   (1 mark)

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  2. i.  

networks-fur2-2008-vcaa-2-answer

b.ii. 

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a.  

♦♦ Exact data unavailable but “few students” answered this question correctly.

 

b.i.    networks-fur2-2008-vcaa-2-answer

 

b.ii.   

MARKER’S COMMENT: Be specific! Note that “an Eulerian circuit requires all vertices of an even degree” did not gain a mark here.