Geodesic
On the uniqueness of exact vertex extensions
Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 81-82 
M. B. Abrosimov; A. A. Dolgov. On the uniqueness of exact vertex extensions. Prikladnaâ diskretnaâ matematika, no. 13 (2011), pp. 81-82. http://geodesic.mathdoc.fr/item/PDM_2011_13_a40/
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     author = {M. B. Abrosimov and A. A. Dolgov},
     title = {On the uniqueness of exact vertex extensions},
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     year = {2011},
     number = {13},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2011_13_a40/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The paper discusses the uniqueness of the exact vertex extensions of graphs. This problem is closely related to reconstruction of graphs. For undirected graphs, the uniqueness has been proved earlier. For oriented graphs, full solution is not known. The obtained result means that if there is a digraph $G$ with the number of vertices greater than 2, which has two or more nonisomorphic 1-vertex exact extansions, the number of vertices of the digraph $G$ is not less than 13, and exact vertex 1-extensions are not reconstructible and do not belong to any known family of nonreconstructible digraphs.

[1] Abrosimov M. B., “Minimalnye rasshireniya dopolnenii grafov”, Teoreticheskie zadachi informatiki i ee prilozhenii, 4, Izd-vo Sarat. un-ta, Saratov, 2001, 11–19

[2] Abrosimov M. B., “Minimalnye rasshireniya tranzitivnykh turnirov”, Vestnik Tomskogo gosuniversiteta, 2006, Prilozhenie No 17, 187–190

[3] Abrosimov M. B., Dolgov A. A., “Tochnye rasshireniya nekotorykh turnirov”, Vestnik Tomskogo gosuniversiteta, 2007, Prilozhenie No 23, 211–216

[4] Stockmeyer P., “A Census of non-reconstructable digraphs, I: six related families”, J. Combinat. Theory, 31 (1981), 232–239 | DOI | MR | Zbl