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Graph algebras and graph varieties. (English) Zbl 0725.08002
Let \(G=(V,E)\) be a directed graph without multiple edges, V denotes the set of vertices, E is the set of edges. Let \(\infty\) be an adjoined element. The operation \(a,b=a\) if (a,b)\(\in E\) and \(a,b=\infty\) otherwise defines the graph algebra on \(V\cup \{\infty \}\). The author proves a “Birkhoff-type” theorem: a class of finite directed graphs is a graph variety iff it is closed with respect to finite restricted pointed subproducts and isomorphic copies. Several applications are given.

08B05 Equational logic, Mal’tsev conditions
05C20 Directed graphs (digraphs), tournaments
Full Text: DOI
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