Let G=(V,E) be a connected graph where V is the set of vertices and E is the set of edges. The graph G has a property such that for any two vertices v_i​,v_j​∈V, there is a unique simple path between them. Prove that G is a tree and find the number of spanning trees in G if ∣V∣=n. Additionally, if G is labeled, meaning each vertex v_i​ has a unique label from 1 to n, determine the number of labeled spanning trees that can be formed from G.

Let G=(V,E) be a connected graph where V is the set of vertices and E is the set of edges. The graph G has a property such that for any two vertices v_i​,v_j​∈V, there is a unique simple path between them. Prove that G is a tree and find the number of spanning trees in G if ∣V∣=n.

Additionally, if G is labeled, meaning each vertex v_i​ has a unique label from 1 to n, determine the number of labeled spanning trees that can be formed from G.