Consider the following graph.
The number of faces is
- 5
- 6
- 7
- 8
Show Worked Solution
♦ Mean mark 52%.
Networks, GEN2 2023 VCAA 12
A country has five states,
A graph can be drawn with vertices to represent each of the states.
Edges represent a border shared between two states.
- What is the sum of the degrees of the vertices of the graph above? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Euler's formula,
, holds for this graph. - i. Complete the formula by writing the appropriate numbers in the boxes provided below. (1 mark)
--- 0 WORK AREA LINES (style=lined) ---
- ii. Complete the sentence by writing the appropriate word in the space provided below. (1 mark)
--- 0 WORK AREA LINES (style=lined) ---
Euler’s formula holds for this graph because the graph is connected and ______________. - The diagram below shows the position of state
on a map of this country. - The four other states are indicated on the diagram as 1, 2, 3 and 4.
- Use the information in the graph above to complete the table below. Match the state
and with the corresponding state number and 4 given in the map above. (1 mark)
--- 0 WORK AREA LINES (style=lined) ---
Networks, GEN1 2022 VCAA 4 MC
Consider the graph below.
The number of edges that need to be removed for this graph to be planar is
- 0
- 1
- 2
- 3
- 4
Show Worked Solution
♦♦♦ Mean mark 21%.
NETWORKS, FUR1 2021 VCAA 3 MC
Consider the graph below.
The number of faces is
- 2
- 3
- 4
- 5
- 6
Show Worked Solution
♦ Mean mark 34%.
NETWORKS, FUR1-NHT 2019 VCAA 6 MC
Four graphs are shown below.
How many of these graphs are planar?
- 0
- 1
- 2
- 3
- 4
Show Worked Solution
NETWORKS, FUR1 2019 VCAA 4 MC
Two graphs, labelled Graph 1 and Graph 2, are shown below.
Which one of the following statements is not true?
- Graph 1 and Graph 2 are isomorphic.
- Graph 1 has five edges and Graph 2 has six edges.
- Both Graph 1 and Graph 2 are connected graphs.
- Both Graph 1 and Graph 2 have three faces each.
- Neither Graph 1 nor Graph 2 are complete graphs.
NETWORKS, FUR1 2018 VCAA 6 MC
Which one of the following graphs is not a planar graph?
| A. |  |
B. |  |
| C. |  |
D. |  |
| E. |  |
NETWORKS, FUR1 2016 VCAA 5 MC
Consider the planar graph below.
Which one of the following graphs can be redrawn as the planar graph above?
NETWORKS, FUR1 2006 VCAA 8 MC
Euler’s formula, relating vertices, faces and edges, does not apply to which one of the following graphs?
Show Worked Solution
♦♦ Mean mark 28%.
MARKER’S COMMENT: Over a third of students incorrectly chose option
MARKER’S COMMENT: Over a third of students incorrectly chose option
NETWORKS, FUR1 2008 VCAA 7 MC
The graph above has
- 4 faces.
- 5 faces.
- 6 faces.
- 8 faces.
- 9 faces.
Show Worked Solution
NETWORKS, FUR1 2011 VCAA 5 MC
A network is represented by the following graph.
Which of the following graphs could not be used to represent the same network?
NETWORKS, FUR1 2014 VCAA 6-7 MC
NETWORKS, FUR1 2015 VCAA 5 MC
The graph below represents a friendship network. The vertices represent the four people in the friendship network: Kwan (
An edge represents the presence of a friendship between a pair of these people. For example, the edge connecting
Which one of the following graphs does not contain the same information?
