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

Erkko Lehtonen; Tamás Waldhauser

doi:10.1007/s10801-020-01010-w

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

Erkko Lehtonen, Tamás Waldhauser

CMA - Centro de Matemática e Aplicações

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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.

Original language	English
Pages (from-to)	613-638
Number of pages	26
Journal	Journal of Algebraic Combinatorics
Volume	53
Issue number	3
DOIs	https://doi.org/10.1007/s10801-020-01010-w
Publication status	Published - May 2021

Keywords

Associative spectrum
Catalan number
DFS tree
Graph algebra

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Lehtonen-Waldhauser2021_Article_AssociativeSpectraOfGraphAlgebFinal published version, 744 KBLicence: CC BY

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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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KW - Catalan number

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

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Keywords

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