Hyperidentities in (xx)y ≈ x(yx) Graph Algebras of Type (2; 0): W. Hemvong, T. Poomsa-ard - Team, Support (Thai Journal of Mathematics, 2007)
Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). A graph G satisfies an identity s ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. G is called a (xx)y ≈ x(yx) graph if A(G) satisfies the equation (xx)y ≈ x(yx). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A if whenever the operation symbols occurring in s and t are replaced by any term operations of A of the appropriate arity, the resulting identities hold in A.In this paper we characterize (xx)y ≈ x(yx) graph algebras, identities and hyperidentities in (xx)y ≈ x(yx) graph algebras.