The existence of perfect codes in Doob graphs

10/09/2018

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by   Denis S. Krotov, et al.

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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.