Critical groups of graphs with reflective symmetry

Authors:
Andrew Berget
Affiliations:
Department of Mathematics, University of Washington, Seattle, US
Venue:
Journal of Algebraic Combinatorics: An International Journal
Year:
2014

Citing 2
Cited 0

The number of spanning trees of plane graphs with reflective symmetry

Journal of Combinatorial Theory Series A
Enumerating spanning trees of graphs with an involution

Journal of Combinatorial Theory Series A

Quantified Score

Hi-index	0.00

Visualization

Abstract

The critical group of a graph is a finite Abelian group whose order is the number of spanning forests of the graph. For a graph G with a certain reflective symmetry, we generalize a result of Ciucu---Yan---Zhang factorizing the spanning tree number of G by interpreting this as a result about the critical group of G. Our result takes the form of an exact sequence, and explicit connections to bicycle spaces are made.