Geodesic
Critical groups of arithmetical structures on star graphs and complete graphs
Kassie Archer1 ; Alexander Diaz-Lopez2 ; Darren Broderick Glass3 ; Joel Louwsma4
1United States Naval Academy
2Villanova University
3Gettysburg College
4Niagara University
The electronic journal of combinatorics, Tome 31 (2024) no. 1
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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.
DOI : 10.37236/11729
Classification : 05C25, 05C50, 11C20, 11D68, 20K01
Mots-clés : finite abelian groups, star graphs, complete graphs

Kassie Archer  1   ; Alexander Diaz-Lopez  2   ; Darren Broderick Glass  3   ; Joel Louwsma  4

1 United States Naval Academy
2 Villanova University
3 Gettysburg College
4 Niagara University 
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     title = {Critical groups of arithmetical structures on star graphs and complete graphs},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
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     doi = {10.37236/11729},
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     url = {http://geodesic.mathdoc.fr/articles/10.37236/11729/}
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Kassie Archer; Alexander Diaz-Lopez; Darren Broderick Glass; Joel Louwsma. Critical groups of arithmetical structures on star graphs and complete graphs. The electronic journal of combinatorics, Tome 31 (2024) no. 1. doi: 10.37236/11729

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