FullSail Mathematics Graph Theory Project Help Download and read the GraphTheory.pdf for complete instructions for the project.Download the P2-Answersheet.

FullSail Mathematics Graph Theory Project Help Download and read the GraphTheory.pdf for complete instructions for the project.Download the P2-Answersheet.docx and put all questions in templateVisit of the following online drawing resources: Google Drawings or Draw.Io or Lucid Charts (or use a drawing tool of your own choice)Create Graphs described in the project and include them in the document Graph Theory Project – Answers
Name(s):
Section:
Research
1. Answer goes here
2. Answer goes here
3. Answer goes here
4. Answer goes here
5. Answer goes here
Analyze
6. There [is / is not] a Path from A to D through every vertex
There [is / is not] a Circuit from C to C through every vertex
7. Answer goes here
Draw and Analyze Graphs
8. [Insert Picture here]
regular graph: [yes/no]
total degree:
planar graph: [yes/no]
Graph Theory Project – Answers
9. [Insert Picture here]
regular graph: [yes/no]
total degree:
planar graph: [yes/no]
10. [Insert Picture here]
regular graph: [yes/no]
total degree:
planar graph: [yes/no]
Bonus
[Insert Picture Here]
GRAPH THEORY PROJECT
Discrete Mathematics
Graph Theory Project
Objective
Synthesize topics from Logic, Set Theory, and Matrices to the topic of Graph Theory.
Students will explore the idea of “connectivity” as a property of Discrete Mathematics
Outline
• Read Chapter 10 Research: Graph Theory in Zybooks
• Answer the questions below
• Use one of the suggested drawing tool (or one of your choice) to draw any graphs
Instructions
Answer the following questions. Present your answers in a document
Research
1. What are a Vertex and edge of a graph?
2. What does it mean for vertices to be adjacent?
3. What is the degree of a vertex?
4. What is the total degree of a graph?
5. What does it mean for a graph to be regular?
Analyze
6. Consider the following graph
•
Is there a path from A to D that goes through every vertex?
If so, write the path in form
•
Is there a circuit from C back to C that goes through every vertex?
If so, write the circuit in form
7. Consider the following graph
•
What is the k-vertex-connectivity of the graph below?
Graph Theory Project
Draw and Analyze Graphs
8. Draw the graph represented by the following set of Vertices and Edges. Then answer the following questions
V = { A,B,C,D,E,F }
E = { {A,B}, {A,C}, {A,D}, {A,F}, {B,C}, {B,E}, {B,F}, {C,D}, {C,F}, {D,E} }
•
Is the graph a regular graph?
•
•
What is the total degree of the graph?
Is the graph planar?
If so, draw it with a planar embedding
9. Draw the graph represented by the following matrix.
•
•
Is the graph a regular graph?
What is the total degree of the graph?
•
Is the graph planar?
If so, draw it with a planar embedding
10.Draw the graph represented by the adjacency list.
•
•
Is the graph a regular graph?
What is the total degree of the graph?
•
Is the graph planar?
If so, draw it with a planar embedding
A
?
B
D
F
B
?
A
C
E
C
?
D
F
B
D
?
C
E
A
E
?
F
B
D
F
?
E
A
C
Bonus
Draw a graph to represent the paths in the following game screen
Review the example at the top of this link (also in the activity on FSO):
http://www.redblobgames.com/pathfinding/a-star/introduction.html
Graph Theory Project
Submission
•
Name the word document Lastname_FirstName_P2.docx and submit it to Project 2 activity on FSO
(If you embed the graphs into your document, you only need to submit that single file)
•
If you have a document and separate pictures compress all files into a file named Lastname_FirstName_P2.zip
Upload this file to the Project 2 activity of FSO
Rubric
Excellent
Good
Poor
Unacceptable
Questions
(90 points)
Correct answers
are worth 9 points
each.
Incomplete answers
are worth 5-6 points
each.
Incorrect answers
are worth 2-3 points
each.
Missing or off topic
answers are worth 0
points each.
Submission
(10 points)
Submission is well
organized and
complete. (10 pts)
Submission is
somewhat
disorganized or
missing solutions. (5
pts)
Submission is very
disorganized. (2
pts)
No submission given. (0
pts)

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