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Networks, STD2 N2 2024 GEN2 13*

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

The floorplan is represented by the network diagram below.

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

This network diagram is incomplete.
 

Draw the missing vertex and missing edges on the diagram above. Include a label.   (2 marks)

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Show Worked Solution

Networks, STD1 N1 2024 HSC 6 MC

The map shows regions within a country.
 

A network diagram is to be drawn to represent this map. Vertices will be used to indicate each region and edges will be used to represent a border shared between two regions.

How many edges will there be in the network diagram?

  1. \(8\)
  2. \(7\)
  3. \(6\)
  4. \(5\)
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\(B\)

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\(\text{Network diagram:}\)
 

\(\text{Network has 7 edges.}\)

\(\Rightarrow B\)

♦♦ Mean mark 30%.

Networks, STD2 N2 SM-Bank 40

The map below shows seven countries within Central America.
 

Draw a network diagram of the map where seven vertices represent each of the countries on the map and edges represent a border shared between two countries.   (2 marks)

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Show Worked Solution

Networks, STD1 N1 2023 HSC 15

The table shows some of the flight distances (rounded to the nearest 10 km between various Australian cities.

  1. Use the information in the table to complete the network diagram where the edges are labelled with distances.  (2 marks)
     


 

  1. Mahsa wants to travel from Hobart to Darwin. She wants to change planes only once.
  2. Using the network diagram, calculate how many kilometres she will travel by plane.  (1 mark)

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a.  

b.    \(4190\text{ km}\)

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a.

b.    \(\text{Changing planes only once}\Rightarrow H\rightarrow S\rightarrow D\)

\(\text{Kilometres travelled}=1040+3150=4190\text{ km}\)

Networks, STD1 N1 2022 HSC 20

The table below shows the distances, in kilometres, between a number of towns.
 

  1. Using the vertices given, draw a weighted network diagram to represent the information shown in the table.  (2 marks)
     

     
  2. A tourist wishes to visit each town.
  3. Draw the minimum spanning tree which will allow for this AND determine its length.  (3 marks)
     

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  1.  
     
     
  2.   
     
  3. `1015\ text{km}`
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a. 

b.   `text{Using Prim’s algorithm (starting at}\ Y):`

`text{1st edge:}\ YC`

`text{2nd edge:}\ CB`

`text{3rd edge:}\ SB`

`text{4th edge:}\ YM`

`text{Length of minimum spanning tree}`

`=275 + 150+60+530`

`=1015\ text{km}`

Networks, STD1 N1 2020 HSC 1 MC

Which of the following networks has more vertices than edges?

 

 

  

 
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`C`

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`text{Consider C:}`

`text{Graph has 5 vertices and 4 edges.}`

`=> \ C`

Networks, STD1 N1 2019 HSC 17

A regional airline operates flights in Queensland. Flight times between connected towns are shown in the table.
 


 

Draw a network diagram to show how the towns are connected, with weights on the edges showing the flight times.  (2 marks)

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`text(Edge weights are in minutes duration.)`

Networks, STD2 N2 2018 FUR1 4 MC

Consider the graph below.
 


 

Which one of the following is not a path for this graph?

  1. `PRQTS`
  2. `PRTSQ`
  3. `PTQSR`
  4. `PTRQS`
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`C`

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`text(By trial and error:)`

`text(Consider option)\ C,`

`PTQSR\ text(is not a path because)\ S\ text(to)\ R`

`text(must go through another vertex.)`

`=> C`

Networks, STD2 N2 SM-Bank 28

In central Queensland, there are four petrol stations `A`, `B`, `C` and `D`. The table shows the length, in kilometres, of roads connecting these petrol stations.
 


 

  1. Construct a network diagram to represent the information in the table.  (2 marks)

  2. A petrol tanker needs to refill each station. It starts at Station `A` and visits each station.

     

    Calculate the shortest distance that can be travelled by the petrol tanker. In your answer, include the order the petrol stations are refilled.  (2 marks)

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  1.  
  2. `380\ text(km)`
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a.   

 

b.   `text(Shortest Path from)\ A\ (text(visiting all stations))`

`A – B – D – C`

`text(Distance)` `= 170 + 90 + 120`
  `= 380\ text(km)`

Networks, STD2 N2 SM-Bank 23

A directed network diagram is pictured below.
 

 
The information in the network diagram is used to complete the network table below, with a "0" used to signify that no connection exists. Complete the table.  (2 marks)
 

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Show Worked Solution

Networks, STD2 N2 SM-Bank 22

The table below represents a directed network.
 

 
Complete the network diagram below to accurately reflect the network described in the above table.  (2 marks)
 

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Show Worked Solution

Networks, STD2 N2 SM-Bank 21

The table below represents a network.
 

 
Complete the network diagram below to accurately reflect the information in the above table.  (2 marks)
 

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Show Worked Solution

Networks, STD2 N2 SM-Bank 11

A network of roads between towns shows the travelling times in minutes between towns that are directly connected.
 

 
Complete the shaded cells in the following table so that it represents the information in this network.  (2 marks) 
 

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Show Worked Solution


 
`text(Note the symmetry in this table across the diagonal.)`

Networks, STD2 N2 2009 FUR2 1

The city of Robville is divided into five suburbs labelled as `A` to `E` on the map below. 

A lake which is situated in the city is shaded on the map.

 

NETWORKS, FUR2 2009 VCAA 11

A table is constructed to represent the number of land borders between suburbs.

If there is no land border between two suburbs, the table records a '0'. If there is a single land border between two suburbs, the table records a '1', and if there are two separate land borders between the same two suburbs, the table records a '2'.
 

`{:({:\ qquadAquadBquadCquadDquadE:}),({:(A),(B),(C),(D),(E):}[(0,1,1,1,0),(1,0,1,2,0),(1,1,0,0,0),(1,2,0,0,0),(0,0,0,0,0)]):}`

 

  1. Explain why all values in the final row and final column of the table are zero.  (1 mark)

In the network diagram below, vertices represent suburbs and edges represent land borders between suburbs. 

The diagram has been started but is not finished.

 

Networks, FUR2 2009 VCAA 1_1

  1. The network diagram is missing one edge and one vertex. 

     

    On the diagram

    1. draw the missing edge  (1 mark)
    2. draw and label the missing vertex.  (1 mark)

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  1. `E\ text(has no land borders with other suburbs.)`
  2. i. & ii.
    Networks, FUR2 2009 VCAA 1 Answer
Show Worked Solution

a.   `E\ text(has no land borders with other suburbs.)`

 

b.i. & ii.    Networks, FUR2 2009 VCAA 1 Answer

Networks, STD2 N2 SM-Bank 37

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 `A` to `H` 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.
 

  1. In the network diagram, what is the order of the vertex that represents the Australian Capital Territory (ACT)?  (1 mark)

  2. In the network diagram, Queensland is represented by which letter? Explain why.  (2 marks)

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a.    `1`

b.    `text{NSW is Vertex B (it is connected to the ACT – Vertex D)}`

`=> C\ text{is Victoria as it has degree 2}`

`:.\ text(Queensland is vertex)\ A\ text(as it is connected to)\ B\ text(and has degree 3.)`

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a.     `text {ACT has 1 border (with NSW)}`

`:.\ text(Degree of ACT’s vertex = 1)`
 

b.    `text{NSW is Vertex B (it is connected to the ACT – Vertex D)}`

`=> C\ text{is Victoria as it has degree 2}`

`:.\ text(Queensland is vertex)\ A\ text(as it is connected to)\ B\ text(and has degree 3.)`

Networks, STD2 N2 2015 FUR1 5 MC

The graph below represents a friendship network. The vertices represent the four people in the friendship network: Kwan (K), Louise (L), Milly (M) and Narelle (N).

An edge represents the presence of a friendship between a pair of these people. For example, the edge connecting K and L shows that Kwan and Louise are friends.

Which one of the following graphs does not contain the same information.
 
 

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`D`

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`text(Option D has Kwan and Milly as friends which is not correct.)`

`=> D`

Networks, STD2 N2 2011 FUR1 1 MC

In the network shown, the number of vertices of even degree is

  1. `2`
  2. `3`
  3. `4`
  4. `5`
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`B`

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`text{Vertices with even degrees: 2, 2, 6}`

`=>  B`

Networks, STD2 N2 2017 FUR1 2 MC

Two graphs, labelled Graph 1 and Graph 2, are shown below.
 

 
The sum of the degrees of the vertices of Graph 1 is

  1. two less than the sum of the degrees of the vertices of Graph 2.
  2. one less than the sum of the degrees of the vertices of Graph 2.
  3. equal to the sum of the degrees of the vertices of Graph 2.
  4. two more than the sum of the degrees of the vertices of Graph 2.
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`C`

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`text(Graph 1)`

`∑\ text(degrees)\ = 3 + 3 + 3 + 3 = 12`

`text(Graph 2)`

`∑\ text(degrees)\ = 2 + 2 + 2 + 2 + 2 + 2 = 12`

`=> C`

Networks, STD2 N2 SM-Bank 3 MC

A store manager is directly in charge of five department managers.

Each department manager is directly in charge of six sales people in their department.

This staffing structure could be represented graphically by

A.   a tree.

B.   a path.

C.   a cycle.

D.   a weighted graph.

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`A`

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`=>  A`

Networks, STD2 N2 2010 FUR1 2 MC

 vcaa-networks-fur1-2010-2 

The number of edges in the graph above is

  1. `5`
  2. `7`
  3. `8`
  4. `10`
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`C`

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`text{Edges are represented by lines between vertices.}`

`=>  C`

Networks, STD2 N2 2012 FUR1 1 MC

The sum of the degrees of all the vertices in the graph above is

A.    `6`

B.    `9`

C.   `11`

D.   `12`

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`D`

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`text(Total Degrees)`

`=1 + 3 + 2 + 2 + 2 + 2`

`=12`

`rArr D`