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Author (up) Aracena, J.; Demongeot, J.; Fanchon, E.; Montalva, M. pdf  doi
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  Title On the number of update digraphs and its relation with the feedback arc sets and tournaments Type Journal Article
  Year 2013 Publication Discrete Applied Mathematics Abbreviated Journal Discret Appl. Math.  
  Volume 161 Issue 10-11 Pages 1345-1355  
  Keywords Update digraph; Feedback arc set; Tournament; Update schedule  
  Abstract An update digraph corresponds to a labeled digraph that indicates a relative order of its nodes introduced to define equivalence classes of deterministic update schedules yielding the same dynamical behavior of a Boolean network. In Aracena et al. [1], the authors exhibited relationships between update digraphs and the feedback arc sets of a given digraph G. In this paper, we delve into the study of these relations. Specifically, we show differences and similarities between both sets through increasing and decreasing monotony properties in terms of their structural characteristics. Besides, we prove that these sets are equivalent if and only if all the digraph circuits are cycles. On the other hand, we characterize the minimal feedback arc sets of a given digraph in terms of their associated update digraphs. In particular, for complete digraphs, this characterization shows a close relation with acyclic tournaments. For the latter, we show that the size of the associated equivalence classes is a power of two. Finally, we determine exactly the number of update digraphs associated to digraphs containing a tournament. (C) 2013 Elsevier B.V. All rights reserved.  
  Address Univ Concepcion, CI2 MA & Dept Ingn Matemat, Concepcion, Chile, Email: jaracena@ing-mat.udec.cl;  
  Corporate Author Thesis  
  Publisher Elsevier Science Bv Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0166-218x ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000319029300005 Approved no  
  Call Number UAI @ eduardo.moreno @ Serial 282  
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