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

Erkko Lehtonen, Tamás Waldhauser

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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 languageEnglish
Pages (from-to)613-638
Number of pages26
JournalJournal of Algebraic Combinatorics
Volume53
Issue number3
DOIs
Publication statusPublished - May 2021

Keywords

  • Associative spectrum
  • Catalan number
  • DFS tree
  • Graph algebra

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