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Let G be an undirected complete graph on n vertices, where n > 2. Then, the number of different Hamiltonian cycles in G is equal to
  • a)
    n!
  • b)
  • c)
    1
  • d)
    (n–1)!
Correct answer is option 'B,C'. Can you explain this answer?
Verified Answer
Let G be an undirected complete graph on n vertices, where n > 2. T...
Option (B):
For labeled nodes,

For an undirected complete graph G.
Number of Hamiltonian cycles are 

3 cycles are;
ABCDA
ACBDA
ACDBA
Option (C):
For unlabelled nodes:
Every Hamilton cycle will be simialr. So answer is 1.
Since in question it is not mentioned whether the graph is labeled or not. So both answers are accepted.
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Let G be an undirected complete graph on n vertices, where n > 2. Then, the number of different Hamiltonian cycles in G is equal toa)n!b)c)1d)(n–1)!Correct answer is option 'B,C'. Can you explain this answer?
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