Monoid algebras and graph products

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

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.

• Jezik: Angleški jezik
• Ključne besede: graph products, monoid algebras, power series rings, uniqueness of roots, cancellation property
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.01.2025
• Leto izida: 2025
• Št. strani: 18 str.
• Številčenje: Vol. 8, no. 1, article no. P1.11
• PID: 20.500.12556/RUL-168861
• UDK: 519.17:512
• ISSN pri članku: 2590-9770
• DOI: 10.26493/2590-9770.1816.e85
• COBISS.SI-ID: 234550019
• Datum objave v RUL: 29.04.2025

Gradivo je del revije

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

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.