For the following pairs of networks, determine if Network 2 is a subnetwork of Network 1:
Network 1
Network 2
Network 1
Network 2
Network 1
Network 2
Network 1
Network 2
Determine whether the following networks are connected:
Consider the following network:
State an edge that can be drawn to make this network connected.
After adding this edge, is there now a path from P to Q?
Consider the following network:
State an edge that can be drawn to make this network connected.
After adding this edge, is there now a path from T to P?
For each of the following networks:
State the weight of the edge connecting Q and S.
Calculate the weight of the entire network.
Calculate the weight of the following paths in this network:
Path Y-E-D
Path A-B-Z-X
Path X-C-A-B-Z
Calculate the weight of the following paths in this network:
The path from Y to X
The path from Z to C
The path from B to X
Find the weight of the following subnetworks:
Consider the following network:
Find the weight of the subnetwork that has only the vertices Q, T, W, and any edges between them.
Find the weight of the subnetwork formed by deleting vertices W, U, V, and S, along with all edges connected to these vertices.
For each of the following, construct a network representing the given information:
The following table lists the amount of time it takes to queue up for three rides at an amusement park, and the amount of time it takes to travel between them:
| Carousel | Pirate Ship | Haunted House | |
|---|---|---|---|
| Carousel | 3 | 5 | 4 |
| Pirate Ship | 5 | 13 | 6 |
| Haunted House | 4 | 6 | 11 |
The following table lists the number of termites observed to be moving within and between three sites in 1 hour:
| Destination | ||||
|---|---|---|---|---|
| \text{Nest} | \text{Plains} | \text{Forest} | ||
| Origin | \text{Nest} | 3570 | 325 | 1240 |
| \text{Plains} | 65 | 475 | 965 | |
| \text{Forest} | 410 | 535 | 230 |
The following table lists the number of likes that four friends give to each other's social media posts over a week:
| Receiver | |||||
|---|---|---|---|---|---|
| \text{Rick} | \text{Fan} | \text{Zoya} | \text{Aarav} | ||
| Sender | \text{Rick} | 32 | 12 | 13 | |
| \text{Fan} | 6 | 9 | 4 | ||
| \text{Zoya} | 41 | 53 | 23 | ||
| \text{Aarav} | 11 | 39 | 2 |
The following table lists the fees (as a percentage) charged by a bank to convert between five types of currency:
| USD | AUS | NZD | EUR | YEN | |
|---|---|---|---|---|---|
| USD | 2 | 5 | 4 | 4 | |
| AUS | 2 | 3 | 5 | 4 | |
| NZD | 5 | 3 | 7 | 6 | |
| EUR | 4 | 5 | 7 | 3 | |
| YEN | 4 | 4 | 6 | 3 |
A few colleagues decided to carpool on the way to work. The following map displays the routes between their homes:
Starting from house A, determine the shortest path that visits every house exactly once.
A courier business has to make multiple pick-ups from several stores. The following map displays the routes between the stores:
Stores A and E need immediate pick up. Starting from store A, determine the shortest path to take if visiting every store only once.
A school bus has to pick up students from a certain area. The following map shows the routes connecting the students' houses:
The school bus driver wants to save as much time as possible on his route. If he starts his route at vertex D, determine the shortest path for him to take if passing by each house only once.
A canned goods company has to make drops at every store in an area. The following map displays the routes between the stores:
Starting from store B, determine the shortest path to take if passing by every store only once.
The delivery man has to drop a newspaper at every house in a certain area. The following graph shows the map of that area:
The delivery man wants to be time efficient. If he enters the area at house B and leaves at house G, find the shortest path for him to travel if he passes by each house only once.
The firefighting department received an emergency call about a house fire across town. The following graph shows the local town map:
If the firefighting department is located at vertex L, and the house is at vertex A, find the shortest route between L and A.
The following map shows all possible routes in Mohamad's town. Mohamad travels from his home to his friend's house on a daily basis.
If Mohamad's house is vertex C, and his friend's house is vertex I, determine the shortest path between the two places.
The grocery store has to make a delivery across town. The store is known for its fast delivery. The following graph represents a map of the town:
If the store is at vertex A, and the delivery has to be made to vertex H, state the shortest path between both vertices.
A group is organizing a tour in the park that ends with a picnic. The following graph displays the map of the park:
Since the tour is for the elderly, the group wants the distance from the start of the park (at vertex A), to the picnic area (at vertex J) to be as short as possible. Find the shortest route between these two vertices.
The police department receives a call about a robbery in progress at a grocery store. The following graph shows the map of the town:
If the grocery store is at vertex I, and the nearest police car is located at vertex D, determine the shortest route for the police to follow.
A rock band is planning a tour across several cities. The following table represents the routes and distance between the cities at which they will be performing:
Construct a graph that represents the table.
Hence, find the shortest route for the rock band to take if they start at city A and passing by each city only once.
| Starting City | Ending City | Distance |
|---|---|---|
| A | C | 9 |
| A | F | 6 |
| B | E | 11 |
| B | F | 5 |
| C | D | 3 |
| C | F | 7 |
| E | D | 5 |
| E | F | 8 |
A mailman was allocated an area to deliver the mail to. The following table represents the routes and times between the houses:
Construct a graph based on the table.
Hence, find the quickest route for the mailman to take if he starts at house D, makes the first delivery to house E, and passes by each house only once.
| Starting House | Ending House | Time |
|---|---|---|
| A | B | 11 |
| A | F | 9 |
| A | G | 3 |
| B | F | 5 |
| B | C | 10 |
| C | E | 8 |
| C | G | 6 |
| D | E | 5 |
| D | G | 5 |
| E | G | 7 |