Question #15595

The complete graph k6 has how many different Hamiltonian circuits?
a) 6
b) 720
c) 120
d) 60

Expert's answer

1) Fix the vertex.

2) From each vertex we can go to another, so start on fix

vertex. We have 5 ways for start. Next we have 4 (5 - 1 from starting point to

this point) ways, next 3, 2, 1.

So, we have 5*4*3*2*1 circuits and 6 ways to

choose first vertex.

Answer 6*5*4*3*2*1=720 - b)

2) From each vertex we can go to another, so start on fix

vertex. We have 5 ways for start. Next we have 4 (5 - 1 from starting point to

this point) ways, next 3, 2, 1.

So, we have 5*4*3*2*1 circuits and 6 ways to

choose first vertex.

Answer 6*5*4*3*2*1=720 - b)

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