  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.
