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arXiv · 1612.00007

On the number of maximum independent sets in Doob graphs

Denis Krotov
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Abstract

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 $H(2m+n,4)$.

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Denis Krotov. 2016-11-30. On the number of maximum independent sets in Doob graphs. https://doi.org/10.17377/semi.2015.12.043

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