Question 1

Consider the paths represented by the numbered sequence of edges on the graphs below. Which path represents an Euler circuit?

Accepted Answer

A)  I only 
B)  II only 
C)  Both I and II 
D)  Neither I nor II 
A)  I only 
B)  II only 
C)  Both I and II 
D)  Neither I nor II

Question 2

Draw a graph with eight vertices, with the valence of each vertex being even, that does NOT have an Euler circuit.

Accepted Answer

Answers ma

Question 3

Which of the graphs below have Euler circuits?

Accepted Answer

A)  I only 
B)  II only 
C)  Both I and II 
D)  Neither I nor II 
A)  I only 
B)  II only 
C)  Both I and II 
D)  Neither I nor II

Question 4

The map below shows the territory for a parking control officer. The dots represent parking meters that need to be checked. Which graph would be useful for finding an efficient route?

Accepted Answer

A)   
B)   
C)   
D)   
A)   
B)   
C)   
D)

Question 5

Consider the path represented by the sequence of numbered edges on the graph below. Explain why the path is NOT an Euler circuit.

Accepted Answer

The path is not an E

Question 6

Find the largest number of paths from A to B that do not have any edges in common.

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
A)  1 
B)  2 
C)  3 
D)  4

Question 7

After a major natural disaster, such as a flood, hurricane, or tornado, many tasks need to be completed as efficiently as possible. For which situation below would finding an Euler circuit or an efficient eulerization of a graph be the appropriate mathematical technique to apply?

Accepted Answer

A)  Relief food supplies must be delivered to eight emergency shelters located at different sites in a large city. 
B)  The Department of Public Works must inspect traffic lights at intersections in the city to determine which are still working. 
C)  An insurance claims adjuster must visit 10 homes in various neighborhoods to write reports. 
D)  The Department of Public Works must inspect all streets in the city to remove dangerous debris. 
A)  Relief food supplies must be delivered to eight emergency shelters located at different sites in a large city. 
B)  The Department of Public Works must inspect traffic lights at intersections in the city to determine which are still working. 
C)  An insurance claims adjuster must visit 10 homes in various neighborhoods to write reports. 
D)  The Department of Public Works must inspect all streets in the city to remove dangerous debris.

Consider the paths represented by the numbered sequence of edges on the graphs below. Which path represents an Euler circuit?

Draw a graph with eight vertices, with the valence of each vertex being even, that does NOT have an Euler circuit.

Which of the graphs below have Euler circuits?

The map below shows the territory for a parking control officer. The dots represent parking meters that need to be checked. Which graph would be useful for finding an efficient route?

Consider the path represented by the sequence of numbered edges on the graph below. Explain why the path is NOT an Euler circuit.

Find the largest number of paths from A to B that do not have any edges in common.

After a major natural disaster, such as a flood, hurricane, or tornado, many tasks need to be completed as efficiently as possible. For which situation below would finding an Euler circuit or an efficient eulerization of a graph be the appropriate mathematical technique to apply?

Business Efficiency

Planning and Scheduling

Linear Programming

Exploring Data: Distributions

Exploring Data: Relationships

Data for Decisions

Probability: the Mathematics of Chance

Social Choice: the Impossible Dream

The Manipulability of Voting Systems

Weighted Voting Systems

Electing the President

Fair Division

Apportionment

Game Theory: the Mathematics of Competition

Identification Numbers

Information Science

Growth and Form

Symmetry and Patterns

Tilings

Savings Models

Borrowing Models

The Economics of Resources

Filters

Exam 1: Urban Services

Consider the paths represented by the numbered sequence of edges on the graphs below. Which path represents an Euler circuit?

Draw a graph with eight vertices, with the valence of each vertex being even, that does NOT have an Euler circuit.

Which of the graphs below have Euler circuits?

The map below shows the territory for a parking control officer. The dots represent parking meters that need to be checked. Which graph would be useful for finding an efficient route?

Consider the path represented by the sequence of numbered edges on the graph below. Explain why the path is NOT an Euler circuit.

Find the largest number of paths from A to B that do not have any edges in common.

After a major natural disaster, such as a flood, hurricane, or tornado, many tasks need to be completed as efficiently as possible. For which situation below would finding an Euler circuit or an efficient eulerization of a graph be the appropriate mathematical technique to apply?

Business Efficiency

Planning and Scheduling

Linear Programming

Exploring Data: Distributions

Exploring Data: Relationships

Data for Decisions

Probability: the Mathematics of Chance

Social Choice: the Impossible Dream

The Manipulability of Voting Systems

Weighted Voting Systems

Electing the President

Fair Division

Apportionment

Game Theory: the Mathematics of Competition

Identification Numbers

Information Science

Growth and Form

Symmetry and Patterns

Tilings

Savings Models

Borrowing Models

The Economics of Resources

Filters