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This analysis reveals nonuniversal properties related to gluing constructions in graphs, indicating their significance in graph theory.
The gluing construction for graphs, which is used in algebraic theory of graph grammars and applied in several fields of Computer Science, is a pushout construction in the category of graphs. In addition to the well known universal properties of pushouts also several nonuniversal properties are required in algebraic graph theory. A systematic collection of these nonuniversal properties is presented in this paper.
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Ehrig et al. (1979) studied this question.
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