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Chapter 14: Problem 73

Group members should determine a relationship that exists among some, but not all, members. Did some of you know one another before the course began? Do some of you have the same academic major? Be as creative as possible in determining this relationship. Then create a graph that serves as a model for describing this relationship.

Short Answer

Expert verified
First, identify a unique relationship within the group by gathering and analyzing information about group members. Then, create a graph or model that represents this relationship. Ensure the final graph is clear, accurate and provides a visual representation of the identified relationship. The specific format of the graph will depend on the relationship identified.

Step by step solution

01

Identifying Relationships

The first step is to gather information from each group member. This could be done through a discussion or a more structured survey. We might look for potential common factors such as prior acquaintance, shared academic major, shared hobbies, or any other factor you can think of. The idea is to be creative and see if there are any relationships that might not be immediately apparent.
02

Analyzing Relationships

Now, take the information you've gathered and analyze it. Are there any relationships that stand out? If yes, then you've found the relationship that you can use for your model. If not, you might need to gather more data or try to think of other, perhaps less obvious, possible relationships with the group members.
03

Creating a Model

Once you've identified your relationship, the next step is to create a model. This could be as simple as a Venn diagram, where one circle represents the entire group and the other represents those within the group who share a certain trait. Alternatively, if your relationship is more complex, you may need to create a more detailed graph that utilizes different types of nodes and edges to better represent the different relationships.
04

Finalizing the Graph

This final step involves finalizing your graph to make sure it is easily readable, accurate, and reflects the relationship you've identified. Don鈥檛 forget to label it properly. This might involve adjusting the sizing, labeling important aspects of the relationship or including a key if necessary.

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Most popular questions from this chapter

In Exercises 11-16, a graph with no loops or more than one edge between any two vertices is described. Which one of the following applies to the description? i. The described graph is a tree. ii. The described graph is not a tree. iii. The described graph may or may not be a tree. The graph has five vertices, and there is exactly one path from any vertex to any other vertex.

Eight students form a math homework group. The students in the group are Zeb, Stryder, Amy, Jed, Evito, Moray, Carrie, and Oryan. Prior to forming the group, Stryder was friends with everyone but Moray. Moray was friends with Zeb, Amy, Carrie, and Evito. Jed was friends with Stryder, Evito, Oryan, and Zeb. Draw a graph that models pairs of friendships among the eight students prior to forming the math homework group.

In Exercises 11-16, a graph with no loops or more than one edge between any two vertices is described. Which one of the following applies to the description? i. The described graph is a tree. ii. The described graph is not a tree. iii. The described graph may or may not be a tree. The graph has eight vertices and five edges.

In Exercises 11-16, a graph with no loops or more than one edge between any two vertices is described. Which one of the following applies to the description? i. The described graph is a tree. ii. The described graph is not a tree. iii. The described graph may or may not be a tree. The graph has five vertices, is connected, and every edge is a bridge.

In Exercises 45-47, you have three errands to run around town, although in no particular order. You plan to start and end at home. You must go to the bank, the post office, and the market. Distances, in miles, between any two of these locations are given in the table. $$ \begin{aligned} &\text { DISTANCES (IN MILES) BETWEEN LOCATIONS }\\\ &\begin{array}{|l|c|c|c|c|} \hline & \text { Home } & \text { Bank } & \text { Post Office } & \text { Market } \\ \hline \text { Home } & * & 3 & 5.5 & 3.5 \\ \hline \text { Bank } & 3 & * & 4 & 5 \\ \hline \text { Post Office } & 5.5 & 4 & * & 4.5 \\ \hline \text { Market } & 3.5 & 5 & 4.5 & * \\ \hline \end{array} \end{aligned} $$ Use the Brute Force Method to find the shortest route to run your errands and return home. What is the minimum distance you can travel?
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