Let G be a connected undirected weighted graph. Consider the following two statements.

S₁: There exists a minimum weight edge in G which is present in every minimum spanning tree of G.

S₂: If every edge in G has distinct weight, then G has a unique minimum spanning tree. Which one of the following options is correct?

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 _______.