Affiliations: [a] Department of Mathematics and Statistics, University of North Florida, Jacksonville, FL 32224, USA. d.genova@unf.edu | [b] LIACS, Leiden University, The Netherlands. h.j.hoogeboom@liacs.leidenuniv.nl | [c] Department of Mathematics and Statistics, University of South Florida, Tampa, USA. jonoska@math.usf.edu
Correspondence:
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Address for correspondence: LIACS, Leiden University, The Netherlands
Abstract: For a family of sets we consider elements that belong to the same sets within the family as companions. The global dynamics of a reactions system (as introduced by Ehrenfeucht and Rozenberg) can be represented by a directed graph, called a transition graph, which is uniquely determined by a one-out subgraph, called the 0-context graph. We consider the companion classes of the outsets of a transition graph and introduce a directed multigraph, called an essential motion, whose vertices are such companion classes. We show that all one-out graphs obtained from an essential motion represent 0-context graphs of reactions systems with isomorphic transition graphs. All such 0-context graphs are obtained from one another by swapping the outgoing edges of companion vertices.
Keywords: directed graphs, graph isomorphism, graphs on posets, dynamics of reaction systems, equivalence of reaction systems
