Geodesic
Characterization of graphs with a~given number of additional edges in a~minimal 1-vertex extension
Prikladnaâ diskretnaâ matematika, no. 1 (2012), pp. 111-120.

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A graph $G^*$ is $k$-vertex extension of graph $G$ if every graph obtained by removing any $k$ vertices from $G^*$ contains $G$. $k$-Vertex extension of graph $G$ with $n+k$ vertices is called minimal if, among all $k$-vertex extensions of graph $G$ with $n+k$ vertices, it has the minimum possible number of edges. The graphs whose minimal vertex 1-extensions have a specified number of additional edges are studied. A solution is given when the number of additional edges is equal to one, two or three.
Keywords: graph, minimal vertex extension, exact vertex extension, fault tolerance. 
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M. B. Abrosimov. Characterization of graphs with a~given number of additional edges in a~minimal 1-vertex extension. Prikladnaâ diskretnaâ matematika, no. 1 (2012), pp. 111-120. http://geodesic.mathdoc.fr/item/PDM_2012_1_a7/

[1] Hayes J. P., “A graph model for fault-tolerant computing system”, IEEE Trans. Comput., C-25:9 (1976), 875–884 | DOI | MR | Zbl

[2] Harary F., Hayes J. P., “Edge fault tolerance in graphs”, Networks, 23 (1993), 135–142 | DOI | MR | Zbl

[3] Harary F., Hayes J. P., “Node fault tolerance in graphs”, Networks, 27 (1996), 19–23 | 3.0.CO;2-H class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[4] Abrosimov M. B., “O slozhnosti nekotorykh zadach, svyazannykh s rasshireniyami grafov”, Matem. zametki, 88:5 (2010), 643–650 | MR | Zbl

[5] Bogomolov A. M., Salii V. N., Algebraicheskie osnovy teorii diskretnykh sistem, Nauka, M., 1997 | MR | Zbl