@article{1e49429d8bb4489faa2b34fa3fe4fa23,
title = "Associative spectra of graph algebras I: Foundations, undirected graphs, antiassociative graphs",
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.",
keywords = "Associative spectrum, Catalan number, DFS tree, Graph algebra",
author = "Erkko Lehtonen and Tam{\'a}s Waldhauser",
note = "Funding Information: This work was partially supported by the Funda{\c c}{\~a}o para a Ci{\^e}ncia e a Tecnologia (Portuguese Foundation for Science and Technology) through the Project UID/MAT/00297/2019 (Centro de Matem{\'a}tica e Aplica{\c c}{\~o}es) and the Project PTDC/MAT-PUR/31174/2017. Funding Information: Research partially supported by the Hungarian Research, Development and Innovation Office Grant K115518, and by Grant TUDFO/47138-1/2019-ITM of the Ministry for Innovation and Technology, Hungary. Publisher Copyright: {\textcopyright} 2021, The Author(s).",
year = "2021",
month = may,
doi = "10.1007/s10801-020-01010-w",
language = "British English",
volume = "53",
pages = "613--638",
journal = "Journal of Algebraic Combinatorics",
issn = "0925-9899",
publisher = "Springer Netherlands",
number = "3",
}