I was wondering if there is any reference or results on the upper bound of the number of subgraphs in a connected acyclic graph (not directed). For example, consider the following graph $G$ represented as edge list: $\{(S,T),(T,G),(T,B),(B,H),(H,Q)\}$. The number of connected subgraph (i.e., tree) is (represented by the set of vertices): $\{S\}$, $\{T\}$, $\{G\}$, $\{B\}$, $\{S,T\}$, $\{T,G\}$, $\{T,B\}$, $\{S,T,G\}$, $\{B,T,G\}$,$\{S,T,B\}$, $\{S,T,G,B\}$,
$\{T,G,B,H\}$,$\{T,B,H,Q\}$, $\{S,T,B,H\}$,$\{S,T,B,H,G\}$,$\{T,G,B,H,Q\}$,$\{S,T,B,H,Q\}$, and 
$\{S,T,B,H,G,Q\}$.

I find two seemingly relevant answer that can directly answer my questions [1](https://cs.stackexchange.com/questions/87388/number-of-connected-subgraphs-of-g-with-at-most-k0-vertices) and [2](https://math.stackexchange.com/questions/803032/number-of-rooted-subtrees-of-given-size-in-infinite-d-regular-tree) but I'm not sure.

Thanks!