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Unit 2 Individual Project
Assignment Overview
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Type: Individual Project
Unit: Graphs and Trees
Due Date: Tue,1/29/19
Grading Type: Numeric
Points Possible: 120
Points Earned:
Deliverable Length: 12 pages
Assignment Details
Learning Materials
Reading Assignment
My Work:
Online Deliverables: Submissions
Assignment Details
Assignment Description
Complete the following in a paper of 1–2 pages:
1. Consider the following graph:
a. Complete this table by finding the degree of each vertex, and identify whether it is even or odd:
Vertex
Degree
Even/Odd
A
B
C
D
E
F
G
H
b. What is the order of the graph?
c. Construct the 10 x 10 adjacency matrix for the graph.
2. The graph below illustrates a switching network. The weights represent the delay times, in nanoseconds, travelled by a data packet between destinations, represented
by the vertices.
2. The graph below illustrates a switching network. The weights represent the delay times, in nanoseconds, travelled by a data packet between destinations, represented
by the vertices.
a. Complete the following table by finding the shortest distance and the path for that distance from vertex A to the other vertices:
Vertex
Shortest Distance
from A
Path from A
B
C
D
E
F
G
H
I
b. What is the shortest distance between A and J and the path for that distance?
3. The following graph represents a portion of the subway system of a city. The vertices on the graph correspond to subway stations, and the edges correspond to the
rails. Your job is to write a program for a cleaning car to efficiently clean this portion of the subway system.
a. Using Euler’s theorem, explain why it is possible to pass through all of the stations by traversing every rail only once.
b. Using Fleury’s algorithm, provide an optimal path to clean all the rails by passing through them only once.
c. Is it possible to find an optimal path described in question 3b that starts on any station? Explain your answer.
d. Is it possible to find an optimal path described in question 3b that starts and ends at the same station? Explain why or why not.
4. A network engineer lives in City A, and his job is to inspect his company’s servers in various cities. The graph below shows the cost (in U.S. dollars) of travelling
between each city that he has to visit.
a. Find a Hamiltonian path in the graph.
b. Find a Hamiltonian circuit that will allow the engineer to inspect all of the servers. How much will the cost be for his trips?
c. Is there another Hamiltonian circuit that will allow the engineer to inspect all of the servers other than your answer in question 4b? If so, calculate the cost.
a. Find a Hamiltonian path in the graph.
b. Find a Hamiltonian circuit that will allow the engineer to inspect all of the servers. How much will the cost be for his trips?
c. Is there another Hamiltonian circuit that will allow the engineer to inspect all of the servers other than your answer in question 4b? If so, calculate the cost.
5. Consider the following binary tree:
a.
b.
c.
d.
What is the height of the tree?
What is the height of vertex H?
Write the preorder traversal representation of the tree.
Write the array representation of the tree by completing the following table:
Vertex
Left Child
Right Child
A
B
C
D
E
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
Please submit your assignment.
For assistance with your assignment, please use your text, Web resources, and all course materials.
Grading Rubric
Project Criteria
Content
(75%)
Exceeds: 90%–100%
Very Good: 80%–89%
Meets: 70%–79%
Needs Improvement: Below 70%
Response covers all topics indicated
in the assignment and adds
additional content.
Response covers most topics
indicated in the assignment.
Response covers many of the
topics indicated in the
assignment.
Response covers none to some of the
topics indicated in the assignment.
Demonstrates very good written,
visual, or oral skills. Demonstrates
sound expression of topic, main
idea, and purpose. Audience is
usually addressed appropriately.
Language does not interfere with the
communication of ideas and content
relevant to the assignment. Errors in
grammar, spelling, and sentence
structure are present, but do not
distract from the message.
Organization is apparent and mostly
clear. Format is appropriate to
assignment, but not entirely
Demonstrates acceptable
written, visual, or oral skills.
Demonstrates reasonable
expression of topic, main idea,
and purpose. Sometimes,
audience is addressed
appropriately. Language does
not interfere with the
communication of ideas and
content relevant to the
assignment. Errors in grammar,
spelling, and sentence structure
are present and may distract
from the message. Organization
is a bit unclear. Format is
Demonstrates inadequate or partially
proficient application of written, visual, or
oral skills. Demonstrates inadequate or
partial expression of topic, main idea,
and purpose. Audience is often not
addressed appropriately. Language often
impedes the communication of ideas
and content relevant to the assignment.
Errors in grammar, spelling, and
sentence structure are frequent and
often distract from meaning or
presentation. Organization is
inadequate, confusing, and distracting.
The format is inadequate and obscures
Demonstrates outstanding or
exemplary application of written,
visual, or oral skills. Demonstrates
outstanding expression of topic,
main idea, and purpose. Audience is
addressed appropriately. Language
clearly and effectively communicates
Effective
ideas and content relevant to the
Communication
assignment. Errors in grammar,
(10%)
spelling, and sentence structure are
minimal. Organization is clear.
Format is consistently appropriate to
assignment. Presentation and
delivery are confident and persuasive
additional content.
Demonstrates outstanding or
exemplary application of written,
visual, or oral skills. Demonstrates
outstanding expression of topic,
main idea, and purpose. Audience is
addressed appropriately. Language
clearly and effectively communicates
Effective
ideas and content relevant to the
Communication
assignment. Errors in grammar,
(10%)
spelling, and sentence structure are
minimal. Organization is clear.
Format is consistently appropriate to
assignment. Presentation and
delivery are confident and persuasive
(where applicable). The writing was
of collegiate level with no errors in
spelling or grammar.
Supporting
Analysis
(15%)
Analysis exceeds minimum
requirements. Sources are used to
support analysis, are appropriate,
and are properly referenced.
indicated in the assignment.
assignment.
topics indicated in the assignment.
Demonstrates very good written,
visual, or oral skills. Demonstrates
sound expression of topic, main
idea, and purpose. Audience is
usually addressed appropriately.
Language does not interfere with the
communication of ideas and content
relevant to the assignment. Errors in
grammar, spelling, and sentence
structure are present, but do not
distract from the message.
Organization is apparent and mostly
clear. Format is appropriate to
assignment, but not entirely
consistent. The writing was of
collegiate level with two or less
errors in spelling or grammar.
Demonstrates acceptable
written, visual, or oral skills.
Demonstrates reasonable
expression of topic, main idea,
and purpose. Sometimes,
audience is addressed
appropriately. Language does
not interfere with the
communication of ideas and
content relevant to the
assignment. Errors in grammar,
spelling, and sentence structure
are present and may distract
from the message. Organization
is a bit unclear. Format is
inconsistent. The writing was of
collegiate level with several
errors in spelling or grammar.
Demonstrates inadequate or partially
proficient application of written, visual, or
oral skills. Demonstrates inadequate or
partial expression of topic, main idea,
and purpose. Audience is often not
addressed appropriately. Language often
impedes the communication of ideas
and content relevant to the assignment.
Errors in grammar, spelling, and
sentence structure are frequent and
often distract from meaning or
presentation. Organization is
inadequate, confusing, and distracting.
The format is inadequate and obscures
meaning. The writing was less than
collegiate level with numerous errors in
spelling or grammar.
Basic analysis provided to support
assertions. Sources are cited,
appropriate, and properly
referenced.
Limited analysis provided to
support assertions. Some
sources are cited, appropriate,
and properly referenced.
No or inaccurate analysis, no sources
are cited when needed, analysis and/or
sources are not appropriate. When
sources are used, they are not properly
referenced.
Reading Assignment
Click here for Unit 2 suggested reading materials.
Assignment Objectives
Apply critical thinking to various IT scenarios using discrete mathematics and statistics techniques.
Employ Boolean algebra concepts, including Boolean logic and operations on Boolean values.
Other Information
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Extra Credit
View Assignment Rubric
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