Critical groups of arithmetical structures on star graphs and complete graphs
Combinatorics
2024-05-22 v2 Number Theory
Abstract
An arithmetical structure on a finite, connected graph without loops is an assignment of positive integers to the vertices that satisfies certain conditions. Associated to each of these is a finite abelian group known as its critical group. We show how to determine the critical group of an arithmetical structure on a star graph or complete graph in terms of the entries of the arithmetical structure. We use this to investigate which finite abelian groups can occur as critical groups of arithmetical structures on these graphs.
Cite
@article{arxiv.2301.02114,
title = {Critical groups of arithmetical structures on star graphs and complete graphs},
author = {Kassie Archer and Alexander Diaz-Lopez and Darren Glass and Joel Louwsma},
journal= {arXiv preprint arXiv:2301.02114},
year = {2024}
}
Comments
24 pages, 2 figures; v2: minor improvements to exposition