Answer to Question #15595 in Discrete Mathematics for Sujata Roy

Question

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

Answer 1

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)