Critical groups of arithmetical structures under a generalized star-clique operation
| Autor: | Alexander Diaz-Lopez, Joel Louwsma |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Mathematics - Number Theory Rings and Algebras (math.RA) 05C50 (Primary) 05C25 11C20 15B36 20K01 (Secondary) FOS: Mathematics Mathematics - Combinatorics Discrete Mathematics and Combinatorics Combinatorics (math.CO) Number Theory (math.NT) Mathematics - Rings and Algebras Geometry and Topology MathematicsofComputing_DISCRETEMATHEMATICS |
| Zdroj: | Linear Algebra and its Applications. 656:324-344 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2022.10.001 |
| Popis: | An arithmetical structure on a finite, connected graph without loops is given by an assignment of positive integers to the vertices such that, at each vertex, the integer there is a divisor of the sum of the integers at adjacent vertices, counted with multiplicity if the graph is not simple. Associated to each arithmetical structure is a finite abelian group known as its critical group. Keyes and Reiter gave an operation that takes in an arithmetical structure on a finite, connected graph without loops and produces an arithmetical structure on a graph with one fewer vertex. We study how this operation transforms critical groups. We bound the order and the invariant factors of the resulting critical group in terms of the original arithmetical structure and critical group. When the original graph is simple, we determine the resulting critical group exactly. 19 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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