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Consider the following graph:

Number of the Hamiltonian cycles starting and ending point at $ A$ is _______ 

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select m out of m point C(5,5)=1
1*((5-1)!/2)=24/2=12 since for two cycle it equevalent to 1  bz both will be isomorphic (they are unlabled)

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I am not convinced by this. Please explain or please tell me the source from where I can clear this out.