Geodesic
On semi-reconstruction of graphs of connectivity~$2$
Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XII, Tome 497 (2020), pp. 80-99

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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 $G\in \{G_1,G_2\}$. 
@article{ZNSL_2020_497_a3,
     author = {D. V. Karpov},
     title = {On semi-reconstruction of graphs of connectivity~$2$},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {80--99},
     publisher = {mathdoc},
     volume = {497},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_497_a3/}
}
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D. V. Karpov. On semi-reconstruction of graphs of connectivity~$2$. Zapiski Nauchnykh Seminarov POMI, Combinatorics and graph theory. Part XII, Tome 497 (2020), pp. 80-99. http://geodesic.mathdoc.fr/item/ZNSL_2020_497_a3/