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.

Rights

URN

URN:NBN:SI:DOC-VPH7KPFJ

COBISSID

234550019

DOI

10.26493/2590-9770.1816.e85

Added

20.02.2026

Metadata

Citation

APA:

Imrich, Wilfried, Klep, Igor, Smertnig, Daniel (2025). Monoid algebras and graph products. The art of discrete and applied mathematics, volume 8, issue 1, article p1.11, 18 str. URN:NBN:SI:DOC-VPH7KPFJ from http://www.dlib.si

MLA:

Imrich, Wilfried, Klep, Igor, Smertnig, Daniel. "Monoid algebras and graph products." The art of discrete and applied mathematics volume 8. issue 1. article p1.11 (2025) 18 str..
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-VPH7KPFJ>