0 votes 0 votes closed as a duplicate of: GATE CSE 2019 | Question: 12 What is the total number of different Hamiltonian cycles for the complete graph of n vertices? Atul Sharma 1 asked Feb 3, 2019 • closed Oct 11, 2023 by Hira Thakur Atul Sharma 1 1.4k views comment Share Follow See all 0 reply Please log in or register to add a comment.
3 votes 3 votes $\frac{(n-1)!}{2}$ Gaurav sarkar answered Feb 3, 2019 Gaurav sarkar comment Share Follow See 1 comment See all 1 1 comment reply pream sagar commented Feb 3, 2019 reply Follow Share i think in gate question they asked about Hamiltonian cycles in case undirected graph 0 votes 0 votes Please log in or register to add a comment.
2 votes 2 votes (n-1)!/2 Sumit Rana 1 answered Feb 3, 2019 Sumit Rana 1 comment Share Follow See all 2 Comments See all 2 2 Comments reply vtreddytkp commented Feb 3, 2019 reply Follow Share 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.. 0 votes 0 votes Ramij commented Feb 4, 2019 reply Follow Share 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 0 votes 0 votes Please log in or register to add a comment.