Note on standard representation of graphs and graph derivations
We show that a naive notion of abstract graph derivations, based on the idea that two derivations are equivalent iff they are isomorphic, does not allow to extend some relevant properties of concrete derivations to abstract ones. This is the main motivation for the introduction of standard representations of graphs, which are used to define a (more restricted) notion of equivalence among graph morphisms, direct derivations and graph derivations. The properties of the resulting category of abstract graphs are investigated in depth, and the relationship with skeleton subcategories of GRAPHS is worked out.
KeywordsIsomorphism Class Standard Representation Direct Derivation Graph Transformation Abstract Graph
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