Discussiones Mathematicae - General Algebra and Applications (Dec 2020)
Graph Varieties Axiomatized by Semimedial, Medial, and Some Other Groupoid Identities
Abstract
Directed graphs without multiple edges can be represented as algebras of type (2, 0), so-called graph algebras. A graph is said to satisfy an identity if the corresponding graph algebra does, and the set of all graphs satisfying a set of identities is called a graph variety. We describe the graph varieties axiomatized by certain groupoid identities (medial, semimedial, autodistributive, commutative, idempotent, unipotent, zeropotent, alternative).
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