Geodesic
Improvement of exponent estimates for mixing graphs of bijective shift registers over a~set of binary vectors
Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 77-83.

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This article presents new estimates for lengths of simple paths and cycles in the mixing graph $G$ of a bijective shift register over a binary vectors set. Also, some sufficient conditions for primitiveness of $G$ are obtained. An upper bound given earlier for the exponent of $G$ is reduced.
Keywords: mixing graph of transformation, graph diameter, graph exponent. 
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A. M. Dorokhova; V. M. Fomichev. Improvement of exponent estimates for mixing graphs of bijective shift registers over a~set of binary vectors. Prikladnaâ diskretnaâ matematika, no. 1 (2014), pp. 77-83. http://geodesic.mathdoc.fr/item/PDM_2014_1_a8/

[1] Koreneva A. M., Fomichev V. M., “Ob odnom obobschenii blochnykh shifrov Feistelya”, Prikladnaya diskretnaya matematika, 2012, no. 3 (17), 34–40

[2] Sachkov V. N., Tarakanov V. E., Kombinatorika neotritsatelnykh matrits, TVP, M., 2000 | MR | Zbl

[3] Fomichev V. M., “Otsenki eksponentov primitivnykh grafov”, Prikladnaya diskretnaya matematika, 2011, no. 2(12), 101–112