### The existence of perfect codes in Doob graphs [article]

Denis S. Krotov (Sobolev Institute of Mathematics, Novosibirsk, Russia)
<span title="2018-10-09">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We solve the problem of existence of perfect codes in the Doob graph. It is shown that 1-perfect codes in the Doob graph D(m,n) exist if and only if 6m+3n+1 is a power of 2; that is, if the size of a 1-ball divides the number of vertices.
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