On the number of update digraphs and its relation with the feedback arc sets and tournaments
Aracena
J
author
Demongeot
J
author
Fanchon
E
author
Montalva
M
author
2013
English
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.
Update digraph
Feedback arc set
Tournament
Update schedule
WOS:000319029300005
exported from refbase (show.php?record=282), last updated on Thu, 27 Jun 2013 21:20:02 -0400
text
files/259_Aracena_etal2013.pdf
10.1016/j.dam.2012.12.018
Aracena_etal2013
Discrete Applied Mathematics
Discret Appl. Math.
2013
Elsevier Science Bv
continuing
periodical
academic journal
161
10-11
1345
1355
0166-218x