Question 1

Which algorithm will always give the optimal tour for a weighted complete graph?

Accepted Answer

A)  Brute-force algorithm 
B)  Nearest-neighbor algorithm 
C)  Repetitive nearest-neighbor algorithm 
D)  Cheapest-link algorithm 
E)  None of the above. 
A)  Brute-force algorithm 
B)  Nearest-neighbor algorithm 
C)  Repetitive nearest-neighbor algorithm 
D)  Cheapest-link algorithm 
E)  None of the above.

Question 2

Is the graph given below a Complete Graph? Explain.

Accepted Answer

No. There are 10 vertices and

Question 3

-Consider the graph above ; does the graph contain a Hamilton Circuit? Explain.

Accepted Answer

No. Once you travel

Question 4

Consider the weighted graph given below; apply the nearest-neighbor algorithm with vertex C as a starting vertex and give the resulting tour?

Accepted Answer

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

Question 5

The chart below shows the one-way charge for a taxi-cab ride between five different cities. Give the cost of a tour found by applying the repetitive nearest-neighbor algorithm.

Accepted Answer

The answer of The chart below shows the one-way charge...

Question 6

How many distinct Hamilton Circuits, if any, are there in the graph shown below? (Mirror images of a circuit are considered distinct from the circuit.)

Accepted Answer

A)  5 
B)  25 
C)  100 
D)  5! 
E)  None of the above.   
A)  5 
B)  25 
C)  100 
D)  5! 
E)  None of the above.

Question 7

The chart below shows the average travel time in minutes between five different cities in Vermont. Give the total time of a tour found by applying the repetitive nearest-neighbor algorithm.

Accepted Answer

A)  110 
B)  115 
C)  120 
D)  122 
E)  None of the above. 
A)  110 
B)  115 
C)  120 
D)  122 
E)  None of the above.

Question 8

Which of the graphs below has a Hamilton Circuit but does not have an Euler Circuit?

Accepted Answer

A)  Graph 1 
B)  Graph 2 
C)  Graph 3 
D)  Both Graph 1 and Graph 2 
E)  None of the above. 
A)  Graph 1 
B)  Graph 2 
C)  Graph 3 
D)  Both Graph 1 and Graph 2 
E)  None of the above.

Question 9

How many vertices are in a complete graph with 45 edges?

Accepted Answer

The answer of How many vertices are in a complete...

Question 10

How many edges are in the complete graph K15 ?

Accepted Answer

A)  15 
B)  105 
C)  210 
D)  14! 
E)  None of the above. 
A)  15 
B)  105 
C)  210 
D)  14! 
E)  None of the above.

Question 11

For the weighted graph below, apply the nearest-neighbor algorithm with D as the starting point and write the resulting tour.

Accepted Answer

D, B, E, A

Question 12

Which of the following is true?

Accepted Answer

A)  The brute-force algorithm is an inefficient algorithm. 
B)  The nearest-neighbor algorithm is an efficient algorithm. 
C)  The brute-force algorithm always gives the optimal tour. 
D)  (a), (b), and (c) are all true. 
E)  None of the above. 
A)  The brute-force algorithm is an inefficient algorithm. 
B)  The nearest-neighbor algorithm is an efficient algorithm. 
C)  The brute-force algorithm always gives the optimal tour. 
D)  (a), (b), and (c) are all true. 
E)  None of the above.

Question 13

Consider the weighted graph given below; which tour is the optimal tour?

Accepted Answer

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

Question 14

How many vertices are in the complete graph with 66 edges?

Accepted Answer

A)  12 
B)  33 
C)  66 
D)  66! 
E)  None of the above. 
A)  12 
B)  33 
C)  66 
D)  66! 
E)  None of the above.

Question 15

For the weighted graph given below, use the brute-force algorithm to find the optimal tour. Write the tour using vertex A as the starting and ending vertex.

Accepted Answer

A, B, C, D

Question 16

Consider the weighted graph given below; which tour is the optimal tour? - 58 -

Accepted Answer

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

Question 17

For the weighted graph below, apply the cheapest-link algorithm and give its cost.

Accepted Answer

The answer of For the weighted graph below, apply the...

Question 18

How many distinct Hamilton circuits, if any, are there in the graph shown below? (Mirror images of a circuit are considered distinct from the circuit.)

Accepted Answer

A)  2 
B)  8 
C)  28 
D)   7 ! 
E)  None of the above. 
A)  2 
B)  8 
C)  28 
D)   7 ! 
E)  None of the above.

Question 19

For the weighted graph shown below, find the weight of the Hamilton Circuit A, E, D, B, C, A.

Accepted Answer

The answer of For the weighted graph shown below, find...

Question 20

Consider the graph shown below; does the graph contain a Hamilton Circuit? Explain.

Accepted Answer

No. Once you travel

Which algorithm will always give the optimal tour for a weighted complete graph?

Is the graph given below a Complete Graph? Explain.

-Consider the graph above ; does the graph contain a Hamilton Circuit? Explain.

Consider the weighted graph given below; apply the nearest-neighbor algorithm with vertex C as a starting vertex and give the resulting tour?

The chart below shows the one-way charge for a taxi-cab ride between five different cities. Give the cost of a tour found by applying the repetitive nearest-neighbor algorithm.

How many distinct Hamilton Circuits, if any, are there in the graph shown below? (Mirror images of a circuit are considered distinct from the circuit.)

The chart below shows the average travel time in minutes between five different cities in Vermont. Give the total time of a tour found by applying the repetitive nearest-neighbor algorithm.

Which of the graphs below has a Hamilton Circuit but does not have an Euler Circuit?

How many vertices are in a complete graph with 45 edges?

How many edges are in the complete graph K15 ?

For the weighted graph below, apply the nearest-neighbor algorithm with D as the starting point and write the resulting tour.

Which of the following is true?

Consider the weighted graph given below; which tour is the optimal tour?

How many vertices are in the complete graph with 66 edges?

For the weighted graph given below, use the brute-force algorithm to find the optimal tour. Write the tour using vertex A as the starting and ending vertex.

Consider the weighted graph given below; which tour is the optimal tour? - 58 -

For the weighted graph below, apply the cheapest-link algorithm and give its cost.

How many distinct Hamilton circuits, if any, are there in the graph shown below? (Mirror images of a circuit are considered distinct from the circuit.)

For the weighted graph shown below, find the weight of the Hamilton Circuit A, E, D, B, C, A.

Consider the graph shown below; does the graph contain a Hamilton Circuit? Explain.

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Exam 6: The Mathematics of Touring: Traveling Salesman Problems

Which algorithm will always give the optimal tour for a weighted complete graph?

Is the graph given below a Complete Graph? Explain.

-Consider the graph above ; does the graph contain a Hamilton Circuit? Explain.

Consider the weighted graph given below; apply the nearest-neighbor algorithm with vertex C as a starting vertex and give the resulting tour?

The chart below shows the one-way charge for a taxi-cab ride between five different cities. Give the cost of a tour found by applying the repetitive nearest-neighbor algorithm.

How many distinct Hamilton Circuits, if any, are there in the graph shown below? (Mirror images of a circuit are considered distinct from the circuit.)

The chart below shows the average travel time in minutes between five different cities in Vermont. Give the total time of a tour found by applying the repetitive nearest-neighbor algorithm.

Which of the graphs below has a Hamilton Circuit but does not have an Euler Circuit?

How many vertices are in a complete graph with 45 edges?

How many edges are in the complete graph K15 ?

For the weighted graph below, apply the nearest-neighbor algorithm with D as the starting point and write the resulting tour.

Which of the following is true?

Consider the weighted graph given below; which tour is the optimal tour?

How many vertices are in the complete graph with 66 edges?

For the weighted graph given below, use the brute-force algorithm to find the optimal tour. Write the tour using vertex A as the starting and ending vertex.

Consider the weighted graph given below; which tour is the optimal tour? - 58 -

For the weighted graph below, apply the cheapest-link algorithm and give its cost.

How many distinct Hamilton circuits, if any, are there in the graph shown below? (Mirror images of a circuit are considered distinct from the circuit.)

For the weighted graph shown below, find the weight of the Hamilton Circuit A, E, D, B, C, A.

Consider the graph shown below; does the graph contain a Hamilton Circuit? Explain.

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 Getting Around: Euler Paths and Circuits

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

Filters