Geodesic
Graph Varieties Axiomatized by Semimedial, Medial, and Some Other Groupoid Identities
Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 2, pp. 143-157

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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).
Keywords: graph algebra, groupoid, identities, semimediality, mediality 
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Lehtonen, Erkko; Manyuen, Chaowat. Graph Varieties Axiomatized by Semimedial, Medial, and Some Other Groupoid Identities. Discussiones Mathematicae. General Algebra and Applications, Tome 40 (2020) no. 2, pp. 143-157. http://geodesic.mathdoc.fr/item/DMGAA_2020_40_2_a0/