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For the graph shown in Fig. 6-19,
a. find three different Hamilton circuits.
b. find a Hamilton path that starts at A and ends at B.
c. find a Hamilton path that starts at D and ends at F.
(a)
To find:
Three Hamilton circuits for given graph.
Answer to Problem 1E
Solution:
The Hamilton circuit are
Explanation of Solution
Given:
The given figure is,
Approach:
A Hamilton circuit is the circuit that starts and ends at the same vertex and includes every other vertex of the graph only once.
Calculation:
Let’s start with vertex A the options to go forward are vertices B, D, F, and G, go to vertex B. From vertex B the options to move further are C, D, E, and G, go to vertex D. From vertex D the option to go forward is vertex C. From vertex C the option to move forward to is E. From vertex E the option to move forward to is F. From vertex F the option to move forward to is G. From vertex G the option to move forward to is A.
The Hamilton circuit is
Let’s start with vertex A the options to go forward are vertices B, D, F, and G, go forward with vertex G. From vertex G the options to move further are B and F, go forward with vertex B. From vertex B the options to go forward are vertices C, D, and E, go to vertex D. From vertex D the option to move forward to is C. From vertex C the option to move forward to is E. From vertex E the option to move forward to is F. From vertex F the option to move forward to is A.
The Hamilton circuit is
Let’s start with vertex A the options to go forward are vertices B, D, F, and G, go forward with vertex D. From vertex D the options to move further are B and C, go forward with vertex B. From vertex B the options to go forward are vertex C and E, go to vertex E. From vertex E the option to move forward to is C. From vertex C the option to move forward to is F. From vertex F the option to move forward to is G. From vertex G the option to move forward to is A.
The Hamilton circuit is
Conclusion:
Thus, the Hamilton circuits are
(b)
To find:
A Hamilton path that starts at A and ends at B.
Answer to Problem 1E
Solution:
A Hamilton path that starts at A and ends at B is
Explanation of Solution
Given:
The given figure is,
Approach:
A Hamilton path is the path that includes every other vertex of the graph only once.
Calculation:
Let’s start with vertex A the options to go forward are vertices B, D, F, and G, go forward with vertex G. From vertex G the options to move further are B and F, go forward with vertex F. From vertex F the options to go forward are vertex C, E, and G, go to vertex E. From vertex E the option to move forward to are B and C, go to vertex C. From vertex C the option to move forward to are B and D, go to vertex D. From vertex D the option to move forward to is B.
The Hamilton path is
Conclusion:
Thus, a Hamilton path that starts at A and ends at B is
(c)
To find:
A Hamilton path that starts at D and ends at F.
Answer to Problem 1E
Solution:
A Hamilton path that starts at D and ends at F is
Explanation of Solution
Given:
The given figure is,
Approach:
A Hamilton path is the path that includes every other vertex of the graph only once.
Calculation:
Let’s start with vertex D the options to go forward are vertices A, B, C, go forward with vertex C. From vertex C the options to move further are B, E and F, go forward with vertex E. From vertex E the options to go forward are vertex B and F, go to vertex B. From vertex B the option to move forward to are A and G, go to vertex G. From vertex G the option to move forward to are A and F, go to vertex A. From vertex A the option to move forward to is F.
The Hamilton path is
Conclusion:
Thus, a Hamilton path that starts at D and ends at F is
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