Acta Applicandae Mathematicae

, Volume 126, Issue 1, pp 245–252 | Cite as

Bi-resolving Graph Homomorphisms and Extensions of Bi-closing codes

Article

Abstract

Given two graphs G and H, there is a bi-resolving (or bi-covering) graph homomorphism from G to H if and only if their adjacency matrices satisfy certain matrix relations. We investigate the bi-covering extensions of bi-resolving homomorphisms and give several sufficient conditions for a bi-resolving homomorphism to have a bi-covering extension with an irreducible domain. Using these results, we prove that a bi-closing code between subshifts can be extended to an n-to-1 code between irreducible shifts of finite type for all large n.

Keywords

Covering Resolving Subamalgamation matrix Covering extension Bi-closing Shift of finite type 

Mathematics Subject Classification (2000)

37B10 05C50 05C70 37B40 

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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of MathematicsAjou UniversitySuwonSouth Korea
  2. 2.The Jesuit Novitiate of St. Stanislaus in KoreaSuwonSouth Korea

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