A graph which is not a single block has at least two leaf blocks.
According to the Intro. to Graph Theory by D. West:
- Block: A maximal connected subgraph of $G$ that has no cut-vertex.
- Leaf block: A block that contains eactly one cut-vertex of $G$.
I have not well understood this statement. Would you elaborate on this statement.
Edit: Can we say this:
The block-cutpoint graph of a connected graph is a tree where its leaves denote the blocks of $G$. Since a tree has at least two leaf blocks hence the graph has at least two leaf blocks if it is not a single block.