Question 1

Find a Hamilton circuit for the figure below.

Accepted Answer

A) ABCDECFA 
B) ABCEDEFA 
C) AFECBDBA 
D) No Hamilton circuit exists. 
A) ABCDECFA 
B) ABCEDEFA 
C) AFECBDBA 
D) No Hamilton circuit exists. D

Question 2

A traveling salesman must visit all four cities indicated in the figure below. How many miles does he travel if he starts in A and then visits B, C, and D before returning to A?

Accepted Answer

A) 892 miles 
B) 1127 miles 
C) 1239 miles 
D) 1273 miles 
A) 892 miles 
B) 1127 miles 
C) 1239 miles 
D) 1273 miles A

Question 3

Find a Hamilton circuit for the figure below.

Accepted Answer

A) ABCDEFA 
B) AFDABCE 
C) AFCDEBA 
D) No Hamilton circuit exists. 
A) ABCDEFA 
B) AFDABCE 
C) AFCDEBA 
D) No Hamilton circuit exists. C

Question 4

A tree has the following characteristic. Find the total number of vertices.

Accepted Answer

A) 13 
B) 18 
C) 20 
D) 26 
A) 13 
B) 18 
C) 20 
D) 26

Question 5

The nearest-neighbor algorithm constructs a(n) _______________ circuit in a complete graph by starting at a vertex.

Accepted Answer

A) Fleury 
B) Euler 
C) Vector 
D) Hamilton 
A) Fleury 
B) Euler 
C) Vector 
D) Hamilton

Question 6

When applying the cheapest-link algorithm, do not choose an edge that would result in a vertex of degree ___.

Accepted Answer

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

Question 7

The _______________ of a vertex is the number of edges that touch that vertex.

Accepted Answer

A) magnitude 
B) amplitude 
C) period 
D) degree 
A) magnitude 
B) amplitude 
C) period 
D) degree

Question 8

Use the nearest-neighbor algorithm starting at vertex A of the figure below to find an approximate solution to the traveling salesman problem.

Accepted Answer

A) ADECBA 
B) ADEBCA 
C) ACBEDA 
D) ABECDA 
A) ADECBA 
B) ADEBCA 
C) ACBEDA 
D) ABECDA

Question 9

A _______________ is a graph that contains no circuits.

Accepted Answer

A) tree 
B) branch 
C) leaf 
D) stem 
A) tree 
B) branch 
C) leaf 
D) stem

Question 10

If each parent of a tree has exactly two children, then the tree is called ___________.

Accepted Answer

A) alternating 
B) binary 
C) equivalent 
D) complete 
A) alternating 
B) binary 
C) equivalent 
D) complete

Question 11

According to Euler's theorem, a connected graph has an Euler circuit precisely when every vertex has a(n) ___________ degree.

Accepted Answer

A) nonzero 
B) positive 
C) even 
D) odd 
A) nonzero 
B) positive 
C) even 
D) odd

Question 12

The following table shows the distance (in miles) between cities A, B, C, and D. When a traveling salesman visits all four cities, how many miles does he travel if he starts in city A and uses the nearest-neighbor algorithm?

Accepted Answer

A) 3885 
B) 3950 
C) 4370 
D) 5135 
A) 3885 
B) 3950 
C) 4370 
D) 5135

Question 13

According to Euler's theorem, the figure below has an Euler circuit.

Accepted Answer

A) True 
 B)False

Question 14

In a complete binary tree of height H, the number of vertices equals _________.

Accepted Answer

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

Question 15

A traveling salesman must visit all four cities indicated in the figure below. When he starts in A, what is the second city to visit according to the nearest-neighbor algorithm?

Accepted Answer

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

Question 16

Which of the following is NOT a leaf in the tree below?

Accepted Answer

A) F 
B) G 
C) H 
D) J 
A) F 
B) G 
C) H 
D) J

Question 17

Estimate the largest number of checks needed if you have a 60,000-word dictionary.

Accepted Answer

A) 14 
B) 15 
C) 16 
D) 17 
A) 14 
B) 15 
C) 16 
D) 17

Question 18

The edges in a certain graph represent roads, and the vertices represent intersections. We want to clean all of the roads and not require the street sweeper to move along streets that have already been cleaned. Should we look for an Euler circuit or a Hamilton circuit?

Accepted Answer

A) Euler 
B) Hamilton 
C) either 
D) neither 
A) Euler 
B) Hamilton 
C) either 
D) neither

Question 19

In a complete binary tree, how many vertices have the level L or

Accepted Answer

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

Question 20

Which of the following is NOT a child in the tree below?

Accepted Answer

A) A 
B) D 
C) G 
D) H 
A) A 
B) D 
C) G 
D) H

Find a Hamilton circuit for the figure below.

A traveling salesman must visit all four cities indicated in the figure below. How many miles does he travel if he starts in A and then visits B, C, and D before returning to A?

Find a Hamilton circuit for the figure below.

A tree has the following characteristic. Find the total number of vertices.

The nearest-neighbor algorithm constructs a(n) _______________ circuit in a complete graph by starting at a vertex.

When applying the cheapest-link algorithm, do not choose an edge that would result in a vertex of degree ___.

The _______________ of a vertex is the number of edges that touch that vertex.

Use the nearest-neighbor algorithm starting at vertex A of the figure below to find an approximate solution to the traveling salesman problem.

A _______________ is a graph that contains no circuits.

If each parent of a tree has exactly two children, then the tree is called ___________.

According to Euler's theorem, a connected graph has an Euler circuit precisely when every vertex has a(n) ___________ degree.

The following table shows the distance (in miles) between cities A, B, C, and D. When a traveling salesman visits all four cities, how many miles does he travel if he starts in city A and uses the nearest-neighbor algorithm?

According to Euler's theorem, the figure below has an Euler circuit.

In a complete binary tree of height H, the number of vertices equals _________.

A traveling salesman must visit all four cities indicated in the figure below. When he starts in A, what is the second city to visit according to the nearest-neighbor algorithm?

Which of the following is NOT a leaf in the tree below?

Estimate the largest number of checks needed if you have a 60,000-word dictionary.

The edges in a certain graph represent roads, and the vertices represent intersections. We want to clean all of the roads and not require the street sweeper to move along streets that have already been cleaned. Should we look for an Euler circuit or a Hamilton circuit?

In a complete binary tree, how many vertices have the level L or

Which of the following is NOT a child in the tree below?

Critical Thinking

Analysis of Growth

Linear and Exponential Change: Comparing Growth Rates

Personal Finance

Introduction to Probability

Statistics

Voting and Social Choice

Geometry

Filters

Exam 7: Graph Theory

Find a Hamilton circuit for the figure below.

A traveling salesman must visit all four cities indicated in the figure below. How many miles does he travel if he starts in A and then visits B, C, and D before returning to A?

Find a Hamilton circuit for the figure below.

A tree has the following characteristic. Find the total number of vertices.

The nearest-neighbor algorithm constructs a(n) _______________ circuit in a complete graph by starting at a vertex.

When applying the cheapest-link algorithm, do not choose an edge that would result in a vertex of degree ___.

The _______________ of a vertex is the number of edges that touch that vertex.

Use the nearest-neighbor algorithm starting at vertex A of the figure below to find an approximate solution to the traveling salesman problem.

A _______________ is a graph that contains no circuits.

If each parent of a tree has exactly two children, then the tree is called ___________.

According to Euler's theorem, a connected graph has an Euler circuit precisely when every vertex has a(n) ___________ degree.

The following table shows the distance (in miles) between cities A, B, C, and D. When a traveling salesman visits all four cities, how many miles does he travel if he starts in city A and uses the nearest-neighbor algorithm?

According to Euler's theorem, the figure below has an Euler circuit.

In a complete binary tree of height H, the number of vertices equals _________.

A traveling salesman must visit all four cities indicated in the figure below. When he starts in A, what is the second city to visit according to the nearest-neighbor algorithm?

Which of the following is NOT a leaf in the tree below?

Estimate the largest number of checks needed if you have a 60,000-word dictionary.

The edges in a certain graph represent roads, and the vertices represent intersections. We want to clean all of the roads and not require the street sweeper to move along streets that have already been cleaned. Should we look for an Euler circuit or a Hamilton circuit?

In a complete binary tree, how many vertices have the level L or

Which of the following is NOT a child in the tree below?

Critical Thinking

Analysis of Growth

Linear and Exponential Change: Comparing Growth Rates

Personal Finance

Introduction to Probability

Statistics

Voting and Social Choice

Geometry

Filters