Graph varieties axiomatized by semimedial, medial, and some other groupoid identities

Discussiones Mathematicae – General Algebra and Applications, 40 (2020), 143–157
http://doi.org/10.7151/dmgaa.1344

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).