Let G be an undirected complete graph on n vertices, where n > 2. Then, the number of different Hamiltonian cycles in G is equal to

Let $$G$$ be a finite group on $$84$$ elements. The size of a largest possible proper subgroup of $$G$$ is ________.

The chromatic number of the following graph is _______.

The minimum number of colours that is sufficient to vertex-colour any planar graph is _____________ .