Cyclic Critical Groups of Graphs

2015/04/22 by Ryan Becker, Becker, Ryan, Darren Glass +1 · 2 citations
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1504.05939

openalex publication_date 2015/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we describe a construction that leads to families of graphs whose critical groups are cyclic. For some of these families we are able to give a formula for the number of spanning trees of the graph, which then determines the group exactly. We also pose several open questions related to this work.

Cited by

• The Smith normal form of Laplacian matrices of simplicial annuli and high dimensional trees
• Generalized chip firing and critical groups of arithmetical structures on trees

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