Particular cycles of a binary de Bruijn digraph
type: Item
instance of: scholarly article
title: Particular cycles of a binary de Bruijn digraph
zbMATH Open document ID: 1223.05140
author: B. E. Eshmatov
published in: European Journal of Combinatorics
publication date: 2010-04-27T00:00:00Z
review text: The authors investigate an isomorphism \(\sigma \) between a directed de Bruijn digraph \(B(2,n)\) and its converse, which is the digraph obtained from \(B(2,n)\) by reversing the direction of all its arcs. A cycle \(C\) is said to be \(\sigma \)-self-converse when the cycle \(\sigma (C)\) coincides with its converse. A characterization is determined of \(\sigma \)-self-converse cycles, distinguishing the cases of \(n\) even and odd. Moreover it is proved that, for \(n\) even, there does not exist a Hamiltonian \(\sigma \)-self-converse cycle, while, for \(n\) odd, we determine a constructive proof of the existence of a similar cycle. Finally they prove that for every \(n\) there exists only one \(\sigma \)-self-converse cycle of length 4.
reviewed by: Michael Hager
Mathematics Subject Classification ID: 05C38
Mathematics Subject Classification ID: 05C20
zbMATH DE Number: 5702102
zbMATH Keywords: binary de Bruijn digraph
zbMATH Keywords: cycle
MaRDI profile type: Publication
full work available at URL: j.ejc.2009.03.026
OpenAlex ID: W2038935338
cites work: Binary de Bruijn cycles under different equivalence relations
cites work: A note on recursive properties of the de Bruijn, Kautz and FFT digraphs
cites work: On a Homomorphism of the de Bruijn Graph and its Applications to the Design of Feedback Shift Registers
DOI: 10.1016/J.EJC.2009.03.026
description: scientific article; zbMATH DE number 5702102