Generalized de Bruijn graphs-Reference-Cited by-同舟云学术

Generalized de Bruijn graphs

Published:2022-02-01 Issue:1 Volume:32 Page:11-38
ISSN:0924-9265
Container-title:Discrete Mathematics and Applications
language:en
Short-container-title:

Author:

Malyshev Fedor M.¹

Affiliation:

1. Steklov Mathematical Institute of Russian Academy of Sciences , Moscow , Russia

Abstract

Abstract We study the graphs of transitions between states of nonautonomous automata that provide, with independent equiprobable input signs, an equiprobable distribution on the set of all states in the minimum possible number of cycles, as is the case of the de Bruijn graphs corresponding to shift registers. It is proved that in the case of a binary input alphabet, there are at least 12r−33 pairwise nonisomorphic directed graphs with 2 r vertices that have this property. All graphs of this type with 8 and 9 vertices are found.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics

Link

https://www.degruyter.com/document/doi/10.1515/dma-2022-0002/pdf

Reference23 articles.

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3. Good I. J., “Normal recurring decimals”, J. London Math. Soc., 21:3 (1946), 167-169.

4. Fredricksen H., “A survey of full length nonlinear shift register cycle algorithms”, SIAM Rev., 24:2 (1982), 195-221.

5. Kratko M. I., Strok V. V., “De Bruijn sequences with constraints”, Voprosy kibernetiki. Kombinatornyy analiz i teoriya grafov, 1980, 80-84 (in Russian).

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