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?



Does this graph have a name?
I have seen this called the *Tree Graph* of $G$. It has been investigated by a lot of authors. For example Cummings proved in "Hamilton circuits in tree graphs" IEEE Trans. Circuit Theory,13(1966), pp.82-90, that this graph is Hamiltonian. Holzmann and Harary generalized this to tree graphs of matroids in ["On the Tree Graph of a Matroid"](http://www.jstor.org/stable/2099712).


