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 |
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Pages (from-to) | 613-638 |
Number of pages | 26 |
Journal | Journal of Algebraic Combinatorics |
Volume | 53 |
Issue number | 3 |
DOIs | |
Publication status | Published - May 2021 |
Keywords
- Associative spectrum
- Catalan number
- DFS tree
- Graph algebra