Unit 6 Graph Theory - AssignmentTotal points for Assignment 35 .docx

Unit 6: Graph Theory - Assignment
Total points for Assignment: 35 points. Assignments must be
submitted as a Microsoft Word document and uploaded to the
Dropbox for Unit 6. All Assignments are due by Tuesday at
11:59 PM ET of the assigned Unit.
NOTE: Assignment problems should not be posted to the
Discussion threads. Questions on the Assignment problems
should be addressed to the instructor by sending an email or by
attending office hours.
You must show your work on all problems. If a problem is
worth 2 points and you only show the answer, then you will
receive only 1 point credit. If you use a calculator or online
website, give the source and tell me exactly what you provided
as input. For example, if you used Excel to compute 16 * 16,
state “I typed =16*16 into Excel and got 256. You may type
your answer right into this document.
Part I. Basic Computations
1.
(4 points) The plan for a four-room house is shown below.
Draw a graph that models the connecting relationships between
the areas in the floor plan. [Your graph does not
[Your graph does not need to be fancy. You may use any
drawing software such as Visio or Creatly.com]
Answer:
2.

a. Identify all the vertices in the above graph with odd degree.
Identify the degree of each of these vertices. (2 points)
Answer:
b.
Describe two paths of different lengths that start at vertex A and
which end at vertex F. Specify the length of each path. (2
points)
Answer:
c.
Describe a circuit of length 3. (2 points)
Answer:
d.
Describe two different circuits of length 4 (1 point)
Answer:
3.
Consider this graph:
a. Find an Euler circuit in this graph that starts and ends at
vertex D. (1 point)
Answer:
b. Using Euler’s Rules, explain how you know that this graph
has an Euler Circuit? (1 point)
Answer:
4.
Paths in a zoo are located according to this map. You want to
make sure that you see every exhibit along each path exactly
once.
a. Where should you begin and end so that you do not need to
retrace your steps? Explain how you know where to start and
end. (1 point)

Answer:
Explanation:
b. Find a path such that you do not need to retrace your steps.
(1 point)
Answer:
Part II. Case Study
The Case of the Missing Cookies
This week’s episode of “Patty Madeye Mysteries” is based on
an investigation at a local Girl Sprouts Camp. Apparently, the
Girl Sprout organization has been gearing up for their annual
fund-raising event in which members sell cookies and candy at
local shopping centers. The proceeds from the fund-raising
event are then used to improve the camping facilities (tents,
mess-hall, swimming area) at the camp.
In her investigation, Patty determines that the cookies and
candy were delivered to the camp on Friday and stored in the
camp office. Over the weekend, the camp director moved them
into the refrigerator unit in the mess-hall so that they would not
melt or spoil. The problem is that the camp director, then lost
her keys to the refrigerator unit sometime while walking the
camp paths, shown in the following diagram (triangles represent
camp buildings/tents; lines represent paths):
SHAPE * MERGEFORMAT
Task #1: (4 points) The camp director is in a hurry to find her
keys and she must search along each of the paths. Can you
determine a way for her to travel each trail only once, starting
and ending at her office? If so, describe the path. If not,
explain how you know that there is no such path, then describe
a path in which the camp director MAY retrace her steps.

Answer:
Task #2. (4 points). When camp is not in session, the camp
director lives in a residence close to the camp. If she doesn’t
find her keys on the camp trials, then either they have been
stolen by a squirrel or they are somewhere in her house, shown
below. Since she might have used her keys to open one of the
many doors in her house, she will need to check each door.
Patty has been asked to provide a sketch showing the
relationships between each of the rooms and doors in the house.
Can you draw a graph depicting this relationship?
Answer:
Task #3. (4 points) Can you determine a method for the camp
director to search for her keys in each of the doors of the house
without retracing her steps? If so, describe the path. If not,
explain how you know that there is no such path.
Answer:
Task #4. (8 points) The directors and producers of The Patty
Madeye Mysteries need some background on graph theory, since
they have not yet taken this course. Do some research on graph
theory using the Kaplan Library and the internet and present a
specific application for graph theory besides those presented in
the course. Your answer should be in paragraph form (no
more than 1 page in length) and may include properly cited or
original images. Be sure to explain the specific real-world
application and give a specific example of where this
application has been used.
Hall
Living�Room

Outside
Kitchen
Den
I
F
C
B
D
H

Office
E
Mess-hall
K
J
B
D
L
F

R #7
Room �#6
Room #3
Rm #8
Rm #4
Room #1
Room #2
Room #9
Room #5

PAGE
Copyright 2010 – Kaplan University – All Rights Reserved
5 | Page
Unit 5: Mathematical Recursion - Assignment
Total points for Assignment: 35 points.
Assignments must be submitted as a Microsoft Word document
and uploaded to the Dropbox for Unit 5.
All Assignments are due by Tuesday at 11:59 PM ET of the
assigned Unit.
NOTE: Assignment problems should not be posted to the
Discussion threads. Questions on the Assignment problems
should be addressed to the instructor by sending an email or by
attending office hours.
You must show your work on all problems. If a problem is
worth 2 points and you only show the answer, then you will
receive only 1 point credit. If you use a calculator or online
website, give the source and tell me exactly what you provided
as input. For example, if you used Excel to compute 16 * 16,
state “I typed =16*16 into Excel and got 256. You may type
your answer right into this document.
Part I. Basic Computations
1.
According to the National Education Association
, the average classroom teacher in the US earned $43,837 in
annual salary for the 1999-2000 school year.

a. If the teachers receive an average salary increase of $1096,
write out the first 6 terms of the sequence formed by the
average salaries starting with the 1999-2000 school year.
Explain how you got your answer. (1 point)
Answer:
Explanation:
b.
Write the general form for the sequence. (1 point)
Answer:
Explanation:
c.
Write the recursive formula for an. (1 point)
Answer:
Explanation:
2.
In 1965, Gordon Moore, the cofounder of Intel, predicted that
the number of transistors that could be designed into an
integrated circuit would double every two years
. This result is known as Moore’s Law.
a.
Complete the following table, showing the number of transisters
per circuit for the indicated years.
(1 point)
Year
Number of Transistors
1972
2500
1974

1976
1978
1980
1982
1984
1986
1988
1990
b.
Express this sequence using a recursive formula in which we
can express any term an in terms of the term an-2 (the term 2
years prior). [Hint: Remember that n represents the number of
years since 1970, since n = 2 represents the year 1972. ] (1
point)
Answer:
Explanation:
c.
According to Intel, the Pentium 4 processor circuit, released in
the year 2000, is designed using 42,000,000 transistors.
According to your calculations, is this circuit consistent with
Moore’s Law? Explain your answer. (1 point)
Answer:
Explanation:
3.
Expand the following summation, then evaluate. In your
explanation, describe the steps involved in arriving at your

answer. (5 points)
10
3
26
j
j
=
-
å
Answer:
Explanation:
4.
The sequence formed by the Lucas numbers is as follows:
{1,3,4,7,11,18,...}
. Using proper terminology as you learned in this unit, compare
and contrast the Lucas sequence with the famous Fibonacci
sequence by naming at least one similar property and one
contrasting property. (4 points)
Answer:
Part II. Case Study
The Mystery of the Missing Coulomb
This week Patty Madeye is going to be investigating the theft of
a rare Orange Tiger Coulomb (shown at the right), which is
owned by Madame Levare, who lives in West Floflux.
Since the jewels are quite valuable, Madam Levare stores them

in the vault at the jeweler’s store, West FloFlux GemStone in
downtown West FloFlux. Only certain lockboxes in the vault
were touched – it seems that the thief knew exactly what he was
looking for.
Task #1 – Patty’s first task is to determine the value of the
jewels. She talks to the jeweler who created them and he
estimates the value of the jewels in 1985 (when they were
purchased) at $65,000. The value is thought to increase
(appreciate) by $1500 per year. If this is true, how much would
the jewels be worth in 2010? Explain how you arrived at your
answer. (4 points)
Answer:
Explanation:
Task #2 - Patty talks to the jeweler and discovers that he
remembers the 4-digit combination to the main vault in the store
by writing it down in summation form. Here’s what he wrote:
The combination is written in summation form, but some of the
notation is cut off from where the paper is ripped. You’ll need
to figure out the full equation so that Patty can get into the
vault to investigate. (4 points)
Answer:
Explanation:
Task #3 - Patty notices a pattern in the numbers of the
lockboxes that were touched during the robbery and says that
she thinks that it’s a mathematical sequence. The sequence is
{ 8, 15, 22, 29, …}. Determine whether this is a sequence (as
far as you can tell) and what type (arithmetic or geometric) it
is. Justify your answer by stating the general term for the
sequence. Assuming Patty is correct, can you identify two other
lockboxes that might have been emptied using this sequence? (4
points)
Answer:
Explanation:

Task #4 (8 points) – Patty asks you to find out more
information about the Fibonacci sequence as background for
this week’s episode. Do some research on the Fibonacci
numbers by consulting the Kaplan Library or the internet. Find
two facts or interesting properties about this fascinating topic
and write a 1 page essay describing what you have found.
Possible approaches include:
· The origin of the Fibonacci sequence?
· What is the connection between the Fibonacci sequence and
the golden ratio?
· Does the “golden string” ever repeat?
Answer:
Essay Requirements
· Write your essay in this document – do not save it in a
separate file.
· Your answer should be between 400-500 words (about 1 page
of double-spaced text)
· You must cite all sources (book, website, periodical) using
APA format, however do not use unreliable sources such as
Wikipedia, and Yahoo! Answers.
� Rankings of the States 2009 and Estimates of School
Statistics 2010. (2009). Retrieved October 19, 2010 from
National Education Association, NEA Research:
http://www.nea.org/home/index.html.
� Moore's Law. (2010). Retrieved October 19, 2010 from
Moore's Law and Intel Innovation: http://www.intel.com/about/
companyinfo/museum/exhibits/moore.htm.

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