Geodesic
On the generation of minimal graph extensions by the method of canonical representatives
Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 179-182

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A graph $G^*$ is a $k$-vertex (edge) extension of a graph $G$ if every graph obtained by removing any $k$ vertices (edges) from $G^*$ contains $G$. A $k$-vertex (edge) extension $G^*$ of graph $G$ is said to be minimal if it contains minimum possible vertices and has the minimum number of edges among all $k$-vertex (edge) extension of graph $G$. The paper proposes an algorithm for generating all non-isomorphic minimal vertex (edge) $k$-extensions of a given graph with isomorphism rejection technique by using method of generating canonical representatives.
Keywords: fault tolerance, graph extension, canonical code, generating canonical representatives.
Mots-clés : isomorphism 
@article{PDMA_2019_12_a49,
     author = {I. A. Kamil and H. H. K. Sudani and A. A. Lobov and M. B. Abrosimov},
     title = {On the generation of minimal graph extensions by the method of canonical representatives},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {179--182},
     publisher = {mathdoc},
     number = {12},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2019_12_a49/}
}
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I. A. Kamil; H. H. K. Sudani; A. A. Lobov; M. B. Abrosimov. On the generation of minimal graph extensions by the method of canonical representatives. Prikladnaya Diskretnaya Matematika. Supplement, no. 12 (2019), pp. 179-182. http://geodesic.mathdoc.fr/item/PDMA_2019_12_a49/