SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

Networks, SMB-023

A new housing estate is being developed.

There are five houses under construction in one location.

These houses are numbered as points 1 to 5 below.
 

  
The builders require the five houses to be connected by electrical cables to enable the workers to have a supply of power on each site.

  1. What is the minimum number of edges needed to connect the five houses?  (1 mark)

  2. On the diagram above, draw a connected graph with this number of edges.  (1 mark) 

Show Answers Only

i.   `text(Minimum number of edges = 4)`
 

ii.   `text(One of many possibilities:)`
 

Show Worked Solution

i.   `text(Minimum number of edges = 4)`
 

ii.   `text(One of many possibilities:)`
 

Networks, SMB-022

The following graph with five vertices is a complete graph.
 

How many edges must be removed so that the graph will have the minimum number of edges to remain connected. Explain your answer.   (3 marks)

Show Answers Only

`text{6 edges need to be removed}`

Show Worked Solution

`text(The minimum number of edges for a connected graph with)`

`text{5 vertices is 4 (see one possible example below).}`
 

 
`:.\ text(Edges to be removed)\ = 10-4= 6`

Networks, SMB-021

Consider the following graph.
 

On the diagram above, make this a connected graph, using the smallest number of edges.   (2 marks)

Show Answers Only

`text{Any addition of 3 edges that connects all vertices.}`
 

Show Worked Solution

`text{Any addition of 3 edges that connects all vertices.}`
 

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)

Show Answers Only

i.    `1`

ii.   `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.)`

Show Worked Solution

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

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

ii.   `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.)`