If $\displaystyle |Sp(G)| = 1$, plz prove that $\displaystyle G$ is a tree.
where $\displaystyle Sp(G)$ = {spanning trees of $\displaystyle G$}
Please take no offence at this comment. But from the tenor of your general questions I have to wonder how careful you are in trying to ingest the meaning of the definitions on Graph Theory.
Let me give you a website that may help you: Graph Theory.
To you current question: If one edge is removed from a tree, is it still connected?
What does it mean to span?
What is a minimal span?