ABSTRACT
The number of different Hamiltonian cycles in an undirected graph is (n − 1)!/2, and the directed graph (n − 1)! In general, not every graph is Hamiltonian graph. If there is a Hamiltonian circle graph or path then one of these three conditions must be fulfilled:
1. Bondy-Chvátal theorem2: A graph is Hamiltonian if and only if its closure
is Hamiltonian.