Which of the following networks is a flow network?
For the identified flow network in part (a), which vertex is:
The source
The sink
Consider the given flow network. Which vertex is:
The source
The sink
Complete the table below for the following flow network:
| Vertex | Inflow | Outflow | Maximum Flow |
|---|---|---|---|
| 2 | |||
| 3 | |||
| 4 |
Complete the table below for the following flow network:
| Vertex | Inflow | Outflow | Maximum Flow |
|---|---|---|---|
| 2 | |||
| 3 | |||
| 4 | |||
| 5 |
State the valid cuts on the following networks:
For each of the following flow networks, list each cut with their corresponding capacity:
For each of the following flow networks, list all the valid cuts with their corresponding capacity:
For each network, determine the cut on the network which has the lowest capacity:
For each of the following graphs, find the maximum flow using the max-flow/min-cut theorem or otherwise:
An oil company just received its pipe maps from the engineer in order to connect the oil storage tank (Vertex 1) to its sink (Vertex 7).
Calculate the maximum flow of oil (in litres/hour) through the pipes.
The ventilation system of an apartment is being drafted by the engineer. The following graph represents the ducts and the maximum flow (in litres/second) in each one.
Calculate the maximum flow between the source (Vertex A) and the sink node (Vertex G).
An engineer was given the task to study the rainwater drainage in a certain area. The following graph represents the drains and their maximum capacity in litres per hour.
Calculate the maximum flow of rainwater in the drainage system between Vertex 1 and Vertex 6.
The following graph represents the road map between Balgownie and Kanahooka, and the maximum number of motorists that can travel on each road at one time.
Calculate the maximum number of vehicles that can travel from Balgownie to Kanahooka at a time.
How could the flow of traffic from Balgownie to Kanahooka be improved to cater for the following issues:
Unanderra is currently over supplied.
Wollongong is currently under supplied.
Port Kembla is currently over supplied.
Fairy Meadow is currently under supplied.
A circuit involving a capacitor, three resistors and two inputs is represented by the following network, with the currents given in \text{mA}:
Calculate the maximum current that can flow between Power in and Power out.
Comment on anything you notice about the capacity through various cuts in this network.