GATE2019 [closed]

Question

What is the total number of different Hamiltonian cycles for the complete graph of n vertices?

Answer 1

$\frac{(n-1)!}{2}$

Comments

i think in gate question they asked about Hamiltonian cycles in case undirected graph

Answer 2

(n-1)!/2

Comments

for three vertices possible hamiltonian cycles are 1.abca 2.acba 3.bacb 4.bcab 5.cabc 6.cbac so from given options in question only n! is satisfying..

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yes @vtreddytkp i got also same answer and if (n-1)/2! is the write answer then for three vertices there will be only one hamilton cycle then how the answer is true ?? @arjun sir please clarify it