Associative spectra of graph algebras I

Abstract

Associative spectra of graph algebras are examined with the help of homomorphisms of DFS trees. Undirected graphs are classified according to the associative spectra of their graph algebras; there are only three distinct possibilities: constant 1, powers of 2, and Catalan numbers. Associative and antiassociative digraphs are described, and associative spectra are determined for certain families of digraphs, such as paths, cycles, and graphs on two vertices.

Measuring associativity: graph algebras of undirected graphs

“…Associative spectra of graph algebras were investigated in [18,19]. The main tool in that study was a result of Pöschel and Wessel [22] describing satisfaction of identities in terms of graph homomorphisms.…”

“…The main tool in that study was a result of Pöschel and Wessel [22] describing satisfaction of identities in terms of graph homomorphisms. Since associative spectra of undirected graphs were completely described in [18] (we state this result in Theorem 5.1), we consider ns(A(G)) and sdist(A(G)).…”