Monoid algebras and graph products
In this note, we extend results about unique nth roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified lexicographic product. We show that these results also hold for graphs with countably many finite connected components, as long as every connected component appears only finitely often (up to isomorphism). The proofs are via monoid algebras and generalized power series rings.
Authors
- Wilfried Imrich (ORCID: https://orcid.org/0000-0002-0475-9335)
- Igor Klep (ORCID: https://orcid.org/0000-0001-5245-8484)
- Daniel Smertnig (ORCID: https://orcid.org/0000-0002-5391-2471)
Institutions
- University of Primorska (SI)
- Montanuniversität Leoben (AT)
- Institute of Mathematics, Physics, and Mechanics (SI)
Publication Details
- Journal
- The Art of Discrete and Applied Mathematics
- Published
- 2025-02-10
- DOI
- https://doi.org/10.26493/2590-9770.1816.e85
- Primary Topic
- Rings, Modules, and Algebras
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Austrian Science Fund
- Javna Agencija za Raziskovalno Dejavnost RS