Question 1

For the graph shown below, what is the degree of vertex D?

Accepted Answer

A)  2 
B)  3 
C)  4 
D)  5 
E)  N one of the above. 
A)  2 
B)  3 
C)  4 
D)  5 
E)  N one of the above.

Question 2

Three distinguished faculty members meet four honors students at a local pub. Each faculty member
shakes hands with each student once and only once. Using people as vertices and handshakes as edges,
construct a graph which models this situation.

Accepted Answer

Here is on

Question 3

The graph shown below

Accepted Answer

A)  contains at least one Euler Path. 
B)  contain at least one Euler Circuit. 
C)  is connected but does not contain either an Euler Path or an Euler Circuit. 
D)  is not connected. 
E)  None of the above.   
A)  contains at least one Euler Path. 
B)  contain at least one Euler Circuit. 
C)  is connected but does not contain either an Euler Path or an Euler Circuit. 
D)  is not connected. 
E)  None of the above.

Question 4

-Consider the graph above ; how many paths are there which start at vertex A and end at vertex G?

Accepted Answer

A)  7 
B)  8 
C)  9 
D)  10 
E)  None of the above. 
A)  7 
B)  8 
C)  9 
D)  10 
E)  None of the above.

Question 5

Two math professors and three engineering professors meet at a local pub. Each professor shakes hands with every other professor once and only once. Which of the graphs below models this situation?

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of the above. 
A)    
B)    
C)    
D)    
E)  None of the above.

Question 6

A graph with two vertices of odd degree and three vertices of even degree will always contain at least one Euler Path. This statement is

Accepted Answer

A)  always true. 
B)  always false. 
C)  true only if the graph is connected. 
D)  false only if the graph is connected. 
E)  None of the above. 
A)  always true. 
B)  always false. 
C)  true only if the graph is connected. 
D)  false only if the graph is connected. 
E)  None of the above.

Question 7

Explain why the graph in figure 2 is not an Eulerization of the graph in figure 1.

Accepted Answer

There is no single edge connec

Question 8

For the graph shown below, state the edge list.

Accepted Answer

AB, AC, AD

Question 9

Jim and John decide to play a game. Jim draws a shape consisting only of lines and he asks John to
put his pencil on the drawing and trace each and every line once and only once, without lifting his
pencil. Is John able to complete this task?
  
(a) Yes
(b) No

Accepted Answer

The answer of Jim and John decide to play a...

Question 10

Jim and John decide to play a game. Jim draws a shape consisting only of lines and he asks John to put his pencil on the drawing and trace each and every line once and only once, without lifting his pencil. Is John able to complete this task? Explain.

Accepted Answer

Yes, as the drawing can be tho

Question 11

Your university has installed a new Meditation Garden which consists of several island gardens connected by bridges. A layout of the garden is shown below. You are enrolled in a Buddhism class and your instructor assigns you the following assignment.
Start at the Tranquility Station and walk through the Meditation Gardens. Every time that you cross a bridge you must recite a Buddhist verse. Continue walking through the gardens until you have crossed each and every bridge. End your journey at the Tranquility Station. What is the fewest number of verses that you would need to recite in order to complete the assignment?

Accepted Answer

The answer of Your university has installed a new Meditation...

Question 12

Consider the graph with vertex set   and edge set   Which edges, if any, are adjacent to edge  GT  ?

Accepted Answer

A)   H, S, T 
B)   G H, G S, O T, S T 
C)   A O 
D)   G S, H O, S T 
E)  None of the above. 
A)   H, S, T 
B)   G H, G S, O T, S T 
C)   A O 
D)   G S, H O, S T 
E)  None of the above.

Question 13

-Consider the graph above ; which edges are adjacent to edge  AD  ?

Accepted Answer

A)   AB, AC, AE, BD, CD, ED 
B)   AB, BB, BD, CD, ED 
C)   AB, BD, CD 
D)   AC, A E, BD, BE, ED 
E)  None of the above. 
A)   AB, AC, AE, BD, CD, ED 
B)   AB, BB, BD, CD, ED 
C)   AB, BD, CD 
D)   AC, A E, BD, BE, ED 
E)  None of the above.

Question 14

-Consider the graph above , which edges, if any, are adjacent to edge BC?

Accepted Answer

The answer of  
-Consider the graph above , which...

Question 15

Three countries align with each other and form the Axis of Evil while four other countries align with each other and form the Axis of Good. Which graph models this situation?

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of the above. 
A)    
B)    
C)    
D)    
E)  None of the above.

Question 16

For the graph shown below, what is the edge set E?

Accepted Answer

CI, DE, DI

Question 17

The graph below does not contain an Euler Circuit. How many edges are traveled a second time if an optimal Eulerization is found for the graph?

Accepted Answer

The answer of The graph below does not contain an...

For the graph shown below, what is the degree of vertex D?

Three distinguished faculty members meet four honors students at a local pub. Each faculty member shakes hands with each student once and only once. Using people as vertices and handshakes as edges, construct a graph which models this situation.

The graph shown below

-Consider the graph above ; how many paths are there which start at vertex A and end at vertex G?

Two math professors and three engineering professors meet at a local pub. Each professor shakes hands with every other professor once and only once. Which of the graphs below models this situation?

A graph with two vertices of odd degree and three vertices of even degree will always contain at least one Euler Path. This statement is

Explain why the graph in figure 2 is not an Eulerization of the graph in figure 1.

For the graph shown below, state the edge list.

Jim and John decide to play a game. Jim draws a shape consisting only of lines and he asks John to put his pencil on the drawing and trace each and every line once and only once, without lifting his pencil. Is John able to complete this task? (a) Yes (b) No

Jim and John decide to play a game. Jim draws a shape consisting only of lines and he asks John to put his pencil on the drawing and trace each and every line once and only once, without lifting his pencil. Is John able to complete this task? Explain.

Consider the graph with vertex set and edge set Which edges, if any, are adjacent to edge GT ?

-Consider the graph above ; which edges are adjacent to edge AD ?

-Consider the graph above , which edges, if any, are adjacent to edge BC?

Three countries align with each other and form the Axis of Evil while four other countries align with each other and form the Axis of Good. Which graph models this situation?

For the graph shown below, what is the edge set E?

The graph below does not contain an Euler Circuit. How many edges are traveled a second time if an optimal Eulerization is found for the graph?

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Exam 5: The Mathematics of Getting Around: Euler Paths and Circuits

For the graph shown below, what is the degree of vertex D?

Three distinguished faculty members meet four honors students at a local pub. Each faculty member shakes hands with each student once and only once. Using people as vertices and handshakes as edges, construct a graph which models this situation.

The graph shown below

-Consider the graph above ; how many paths are there which start at vertex A and end at vertex G?

Two math professors and three engineering professors meet at a local pub. Each professor shakes hands with every other professor once and only once. Which of the graphs below models this situation?

A graph with two vertices of odd degree and three vertices of even degree will always contain at least one Euler Path. This statement is

Explain why the graph in figure 2 is not an Eulerization of the graph in figure 1.

For the graph shown below, state the edge list.

Jim and John decide to play a game. Jim draws a shape consisting only of lines and he asks John to put his pencil on the drawing and trace each and every line once and only once, without lifting his pencil. Is John able to complete this task? (a) Yes (b) No

Jim and John decide to play a game. Jim draws a shape consisting only of lines and he asks John to put his pencil on the drawing and trace each and every line once and only once, without lifting his pencil. Is John able to complete this task? Explain.

Consider the graph with vertex set and edge set Which edges, if any, are adjacent to edge GT ?

-Consider the graph above ; which edges are adjacent to edge AD ?

-Consider the graph above , which edges, if any, are adjacent to edge BC?

Three countries align with each other and form the Axis of Evil while four other countries align with each other and form the Axis of Good. Which graph models this situation?

For the graph shown below, what is the edge set E?

The graph below does not contain an Euler Circuit. How many edges are traveled a second time if an optimal Eulerization is found for the graph?

The Mathematics of Elections: the Paradoxes of Democracy

The Mathematics of Power: Weighted Voting

The Mathematics of Sharing: Fair-Division Games

The Mathematics of Apportionment: Making the Rounds

The Mathematics of Touring: Traveling Salesman Problems

The Cost of Being Connected

The Mathematics of Scheduling: Chasing the Critical Path

Population Growth Models: There Is Strength in Numbers

Financial Mathematics: Money Matters

The Mathematics of Symmetry: Beyond Reflection

Fractal Geometry: the Kinky Nature of Nature

Fibonacci Numbers and the Golden Ratio: Tales of Rabbits and Gnomons

Censuses, Surveys, Polls, and Studies: the Joys of Collecting Data

Graphs, Charts, and Numbers: the Data Show and Tell

Probabilities, Odds, and Expectations: Measuring Uncertainty and Risk

The Mathematics of Normality: the Call of the Bell

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