For a graph $G$ on $n \geq 1$ vertices, what is the maximum number of vertices of its block-cutpoint graph $BC(G)$?
What I have so far:
The block-cutpoint graph of a graph $G$ is the bipartite graph which consists of the set of cut-vertices of $G$ and a set of vertices which represent the blocks of $G$.
Let $G=(V,E)$ be a connected graph. Let $v$ be a vertex of $G$. Then $v$ is a cut-vertex of $G$ iff the vertex deletion $G−v$ is a vertex cut of $G$.That is, such that $G−v$ is disconnected.
A block is a maximal biconnected subgraph of a given graph $G$.
I don't really know what else I need to know to solve this.