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 if 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 number of vertices, draw a simple network where every vertex is directly connected to every other vertex by an edge:
2 vertices
3 vertices
4 vertices
5 vertices
Complete the following table for the networks from part (a):
| \text{Vertices, }v | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
| \text{Edges, }e |
State the rule to calculate the number of edges, e, given the number of vertices, v, in a simple connected network.
Calculate the number of edges required for a simple connected network with 10 vertices.
For each of the following networks:
State the weight of the edge connecting Q to 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:
Path from Y to X
Path from Z to C
Path from B to X
Find the weight of the following subnetworks, highlighted in green:
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 |
In graph theory terms, state the definition of:
Determine whether each of the following graphs is a tree. If it is not a tree, explain why.
Sarah has three children: Kate, Matt and Tom. Kate has four children: Lisa, Sandy, Amy and Robert. Matt has two sons: Joseph and Chris. Both Tom and Lisa have one child each: Barbara and Alex, respectively.
If the starting vertex represents Sarah, create a tree to represent the parent-child relationships in this family.
Bianca is writing a report and needs to create a table of contents. Her report consists of five chapters, each broken down into sections:
The first chapter is her introduction, so it has just one section.
Her second and third chapters both have three sections, while the fourth chapter has six sections.
The fifth and final chapter is the conclusion which again has only one section.
Create a tree that represents the structure of Bianca's table of contents.
Mitchell is tracing his family lineage back three generations:
His mother's name is Rebecca, and his father's name is Connor.
Rebecca's parents are Mabel and Patrick, and Connor's parents are Juliet and Mark.
Mitchell does not know Mabel's parents's names, but he knows that Patrick's parents are April and Todd.
On the other side, Mitchell knows that Juliet's parents are Daisy and Leonard, and Mark's dad is called Richard.
Mitchell does not know the name of Mark's mother, however.
If the initial vertex represents Mitchell, create a family tree of the last three generations from the information above. Make sure to include any ancestors that he doesn't know the name of using the word "Unknown".
Determine if the following networks have a spanning tree:
