A Note on an Old-Fashioned Algebra for (Disconnected) Graphs

Authors:
Fabio Gadducci
Affiliations:
Dipartimento di Informatica, Università di Pisa, Polo Universitario “G. Marconi” di La Spezia
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2009

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Abstract

Graphs with interfaces are a simple and intuitive tool for allowing a graph G to interact with the environment, by equipping it with two morphisms J -G, I -G. These ''handles'' were used to define graphical operators, and to provide an inductive presentation of graph rewriting. A main feature of graphs with interfaces is their characterization as terms of a free algebra. So far, this was possible only with discrete interfaces, i.e., containing no edge. This note shows that a similar free construction can be performed also with disconnected interfaces, i.e., containing only nodes connected to at most one edge.