Geodesic
On the number of maximum independent sets in Doob graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 508-512

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The Doob graph $D(m,n)$ is a distance-regular graph with the same parameters as the Hamming graph $H(2m+n,4)$. The maximum independent sets in the Doob graphs are analogs of the distance-$2$ MDS codes in the Hamming graphs. We prove that the logarithm of the number of the maximum independent sets in $D(m,n)$ grows as $2^{2m+n-1}(1+o(1))$. The main tool for the upper estimation is constructing an injective map from the class of maximum independent sets in $D(m,n)$ to the class of distance-$2$ MDS codes in $H(2m+n,4)$.
Keywords: Doob graph, independent set
Mots-clés : MDS code, latin hypercube. 
@article{SEMR_2015_12_a54,
     author = {D. S. Krotov},
     title = {On the number of maximum independent sets in {Doob} graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {508--512},
     publisher = {mathdoc},
     volume = {12},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2015_12_a54/}
}
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D. S. Krotov. On the number of maximum independent sets in Doob graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 12 (2015), pp. 508-512. http://geodesic.mathdoc.fr/item/SEMR_2015_12_a54/