Let $G$ be a connected graph on $n$ vertices and $\mathcal{T}$ be the set of all spanning trees of $G$.

Consider the graph whose vertices are the elements of $\mathcal{T}$ and

$T, T' \in \mathcal{T}$ are connected by an edge if $|E(T)\cap E(T')| = n - 2 $

Does this graph have a name?

One can see that the graph is connected. Are any of its other properties known?

Is there any literature on this graph?