Critical groups of graphs with reflective symmetry
arXiv:1208.0632 · doi:10.1007/s10801-013-0445-x
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.
17 pages. To appear in J. Alg. Comb