Identities in Graph Algebras of Type (n, n − 1, ..., 3, 2, 0)

T. Poomsa-ard, J. Wetweerapong, C. Khiloukom, T. Musuntei

Abstract

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies an identity $s \thickapprox t $ if the corresponding graph algebra A(G) satisfies $s \thickapprox t.$ In this paper we generalize the concept of graph algebras of type $\tau = (2, 0)$ to define graph algebras of type $\tau = (n, n−1, n−2, ..., 3, 2, 0), n \geqslant 2$ and characterize identities in graph algebras. Further we show that any term over the class of all graph algebras can be uniquely represented by a normal form term and that there is an algorithm to construct the normal form term to every given term t.