Additional Topics: Hamiltonian Paths and Cycles A Hamiltonian path in a directed graph is a path that visits every vertex in the graph exactly once. A Hamiltonian cycle in a directed graph is a cycle that visits every vertex in the graph exactly once (except for the vertex at the beginning and end of the cycle). For example, in the following directed graph, 1,3,4,2 is a Hamiltonian path and 1, 3, 4, 2, 1 is a Hamiltonian cycle. Z For more information about Hamiltonian paths and cycles, see zyBook section 13.7. 7. (10 pt.) Given the following directed graphs: G₁ Answer the following questions: • Is there a Hamiltonian path in the graph? If so, find one. • Is there a Hamiltonian cycle in the graph? If so, find one. G3
Additional Topics: Hamiltonian Paths and Cycles A Hamiltonian path in a directed graph is a path that visits every vertex in the graph exactly once. A Hamiltonian cycle in a directed graph is a cycle that visits every vertex in the graph exactly once (except for the vertex at the beginning and end of the cycle). For example, in the following directed graph, 1,3,4,2 is a Hamiltonian path and 1, 3, 4, 2, 1 is a Hamiltonian cycle. Z For more information about Hamiltonian paths and cycles, see zyBook section 13.7. 7. (10 pt.) Given the following directed graphs: G₁ Answer the following questions: • Is there a Hamiltonian path in the graph? If so, find one. • Is there a Hamiltonian cycle in the graph? If so, find one. G3
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.6: Rotations And Symmetry
Problem 1C
Related questions
Question
![Additional Topics: Hamiltonian Paths and Cycles
A Hamiltonian path in a directed graph is a path that visits every vertex in the graph exactly once.
A Hamiltonian cycle in a directed graph is a cycle that visits every vertex in the graph exactly once
(except for the vertex at the beginning and end of the cycle). For example, in the following directed
graph, 1,3,4,2 is a Hamiltonian path and 1, 3, 4, 2, 1 is a Hamiltonian cycle.
Z
For more information about Hamiltonian paths and cycles, see zyBook section 13.7.
7. (10 pt.) Given the following directed graphs:
G₁
Answer the following questions:
• Is there a Hamiltonian path in the graph? If so, find one.
• Is there a Hamiltonian cycle in the graph? If so, find one.
G3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fda22bb93-89e0-43b0-b495-0a6067b20da3%2Fa84693e7-2315-4e20-9b5a-65ab06bfd50b%2Fvwq010p_processed.png&w=3840&q=75)
Transcribed Image Text:Additional Topics: Hamiltonian Paths and Cycles
A Hamiltonian path in a directed graph is a path that visits every vertex in the graph exactly once.
A Hamiltonian cycle in a directed graph is a cycle that visits every vertex in the graph exactly once
(except for the vertex at the beginning and end of the cycle). For example, in the following directed
graph, 1,3,4,2 is a Hamiltonian path and 1, 3, 4, 2, 1 is a Hamiltonian cycle.
Z
For more information about Hamiltonian paths and cycles, see zyBook section 13.7.
7. (10 pt.) Given the following directed graphs:
G₁
Answer the following questions:
• Is there a Hamiltonian path in the graph? If so, find one.
• Is there a Hamiltonian cycle in the graph? If so, find one.
G3
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