On semi-reconstruction of graphs of connectivity $2$

Recall that the deck of a graph $G$ is the collection of subgraphs $G-v$ for all vertices $v$ of the graph $G$. We prove that at most two graphs of connectivity $2$ and minimal degree at least $3$ can have the same deck. Let $\mathcal{D}(G)$ be a deck of a $2$-connected graph $G$. We describe an algorithm which construct by the deck $\mathcal{D}(G)$ of a $2$-connected graph $G$ with minimal degree at least $3$ two graphs $G_1,G_2$ such that $G\in \{G_1,G_2\}$.