Geodesic
About minimal $1$-edge extension of hypercube
Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 109-111

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A hypercube $Q_n$ is a regular $2^n$-vertex graph of order $n$, which is the Cartesian product of $n$ complete $2$-vertex graphs $K_2$. For any integer $n>1$, we define a graph $Q^*_n$ by connecting each vertex $v$ in $Q_n$ with one which is most far from $v$. It is shown that $Q^*_n$ is the minimal $1$-edge extension of the hypercube $Q_n$. The computational experiment shows that for each $n\leq4$ this extension is unique up to isomorphism.
Keywords: graph, edge fault tolerance, minimal $1$-edge extension.
Mots-clés : hypercube 
@article{PDMA_2018_11_a33,
     author = {A. A. Lobov and M. B. Abrosimov},
     title = {About minimal $1$-edge extension of hypercube},
     journal = {Prikladnaya Diskretnaya Matematika. Supplement},
     pages = {109--111},
     publisher = {mathdoc},
     number = {11},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDMA_2018_11_a33/}
}
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A. A. Lobov; M. B. Abrosimov. About minimal $1$-edge extension of hypercube. Prikladnaya Diskretnaya Matematika. Supplement, no. 11 (2018), pp. 109-111. http://geodesic.mathdoc.fr/item/PDMA_2018_11_a33/