Question

In a 7-node directed cyclic graph, the number of Hamiltonian cycle is to be ______

(a) 728

(b) 450

(c) 360

(d) 260

I had been asked this question in a national level competition.

My query is from Graphs Properties in chapter Graphs of Discrete Mathematics

Answer 1

Right option is (c) 360

The explanation is: A Hamiltonian cycle in a connected graph G is defined as a closed path that traverses every vertex of G exactly once except the starting vertex, at which the path also terminates. In an n-complete graph, there are (n-1)!/2 hamiltonian cycles and so the answer is 360.