Consider the following networks:
Network A
Network B
Network C
Determine which network is a flow network.
State the source vertex of the flow network.
State the sink vertex of the flow network.
Consider the given flow network:
Which vertex is the source for this flow network?
Which vertex is the sink for this flow network?
For each of the following flow networks, calculate the inflow, outflow and maximum flow for the indicated vertices:
For vertices 2,3, \text{and } 4
For vertices 2,3, 4,\text{and } 5
For each of the following networks, list all the cuts that are valid:
For each of the following networks, calculate the capacity through each cut:
Determine the capacity through each of the valid cuts of the following flow networks:
For each of the following networks, determine which of the cuts has the smallest capacity:
Calculate the maximum flow through the following networks:
An oil company just received their pipe maps from the engineer connecting 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.
Calculate the maximum flow of rainwater (in litres/hour) 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.
The traffic flow (in hundreds of cars per hour) through a city centre is shown in the following directed network:
Identify the source vertex.
Identify the sink vertex.
Calculate the maximum flow through this network.
A network of water pipes is shown in the first figure, with the maximum flow capacity of each pipe given in litres per minute. The second figure shows a possible flow of water within the network:
Determine the missing values in the second figure.
For the flow shown in second diagram, which pipes are operating at full capacity?
Calculate the total flow for the second diagram.
It is possible to increase the flow from part (c) by 5 \text{ litres/min}. State the path that can support this extra flow.
Determine the flow through each of the cuts P, Q, R and S in the diagram on the right.
State the cut that shows the flow achieved in part (d) is a maximum for this network.