Associative spectra of graph algebras I : Foundations, undirected graphs, antiassociative graphs

Lehtonen, E. and Waldhauser, Tamás (2021) Associative spectra of graph algebras I : Foundations, undirected graphs, antiassociative graphs. JOURNAL OF ALGEBRAIC COMBINATORICS, 53 (3). pp. 613-638. ISSN 0925-9899

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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.

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