Monoid algebras and graph products

Imrich, Wilfried (author), Klep, Igor (author), Smertnig, Daniel (author)

In this note, we extend results about unique $n^{\rm th}$ 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.

• Language: English
• Keywords: graph products, monoid algebras, power series rings, uniqueness of roots, cancellation property
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Publication date: 01.01.2025
• Year: 2025
• Number of pages: 18 str.
• Numbering: Vol. 8, no. 1, article no. P1.11
• PID: 20.500.12556/RUL-168861
• UDC: 519.17:512
• ISSN on article: 2590-9770
• DOI: 10.26493/2590-9770.1816.e85
• COBISS.SI-ID: 234550019
• Publication date in RUL: 29.04.2025

Record is a part of a journal

• Title: The art of discrete and applied mathematics
• Publisher: Fakulteta za matematiko, naravoslovje in informacijske tehnologije
• ISSN: 2590-9770
• COBISS.SI-ID: 290758912

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.