Work

Monoid algebras and graph products

Year: 2025

Type: article

Abstract: 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.

Source: The Art of Discrete and Applied Mathematics

DOI: 10.26493/2590-9770.1816.e85

Authors: Wilfried Imrich, Igor Klep, Daniel Smertnig

Institutions: Montanuniversität Leoben, University of Primorska, University of Ljubljana, Institute of Mathematics, Physics, and Mechanics

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: Austrian Science Fund, Javna Agencija za Raziskovalno Dejavnost RS