Consider the directed network below.
The number of vertices that cannot be reached from `X` is
- 1
- 2
- 3
- 4
- 5
NETWORKS, FUR1 2020 VCAA 4 MC
The directed graph below represents a series of one-way streets.
The vertices represent the intersections of these streets.
The number of vertices that can be reached from `S` is
- 1
- 2
- 3
- 4
- 5
NETWORKS, FUR1 2008 VCAA 1 MC
Steel water pipes connect five points underground.
The directed graph below shows the directions of the flow of water through these pipes between these points.
The directed graph shows that water can flow from
A. point 1 to point 2.
B. point 1 to point 4.
C. point 4 to point 1.
D. point 4 to point 2.
E. point 5 to point 2.
NETWORKS, FUR1 2006 VCAA 2 MC
The following directed graph represents a series of one-way streets with intersections numbered as nodes 1 to 8.
All intersections can be reached from
A. intersection 4
B. intersection 5
C. intersection 6
D. intersection 7
E. intersection 8
NETWORKS, FUR1 2012 VCAA 6 MC
In the digraph above, all vertices are reachable from every other vertex.
All vertices would still be reachable from every other vertex if we remove the edge in the direction from
A. `Q` to `U`
B. `R` to `S`
C. `S` to `T`
D. `T` to `R`
E. `V` to `U`
MATRICES*, FUR1 2013 VCAA 9 MC
Alana, Ben, Ebony, Daniel and Caleb are friends. Each friend has a different age.
The arrows in the graph below show the relative ages of some, but not all, of the friends. For example, the arrow in the graph from Alana to Caleb shows that Alana is older than Caleb.
Using the information in the graph, it can be deduced that the second-oldest person in this group of friends is
A. Alana
B. Ben
C. Caleb
D. Daniel
E. Ebony
Show Worked Solution
`text(Completing the graph,)`
`:.\ text(Oldest to youngest is:)`
`text(Alana, Ben, Daniel, Caleb, Ebony.)`
`=> B`
NETWORKS, FUR1 2014 VCAA 2 MC
In the directed graph above, the only vertex with a label that can be reached from vertex Y is
A. vertex A
B. vertex B
C. vertex C
D. vertex D
E. vertex E
NETWORKS, FUR2 2009 VCAA 2
One of the landmarks in the city is a hedge maze. The maze contains eight statues. The statues are labelled `F` to `M` on the following directed graph. Walkers within the maze are only allowed to move in the directions of the arrows.
- Write down the two statues that a walker could not reach from statue `M`. (1 mark)
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- One way that statue `H` can be reached from statue `K` is along path `KFH`.
List the three other ways that statue `H` can be reached from statue `K`. (1 mark)
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