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).

Keywords

• graph algebra
• groupoid
• identities
• semimediality
• mediality
• 05c25
• 03c05