Critical Groups of Graphs with Dihedral Actions II

Authors

Darren B. Glass, Gettysburg CollegeFollow

Document Type

Article

Publication Date

9-22-2016

Department 1

Mathematics

Abstract

In this paper we consider the critical group of finite connected graphs which admit harmonic actions by the dihedral group D_n, extending earlier work by the author and Criel Merino. In particular, we show that the critical group of such a graph can be decomposed in terms of the critical groups of the quotients of the graph by certain subgroups of the automorphism group. This is analogous to a theorem of Kani and Rosen which decomposes the Jacobians of algebraic curves with a D_n-action.

Copyright Note

This is the author's version of the work. This publication appears in Gettysburg College's institutional repository by permission of the copyright owner for personal use, not for redistribution.

DOI

10.1016/j.ejc.2016.09.010

Version

Post-Print

Recommended Citation

Glass, Darren. "Critical Groups of Graphs with Dihedral Actions II." European Journal of Combinatorics 61 (March 2017): pp. 25-46.

Required Publisher's Statement

Original version available from the publisher at: http://www.sciencedirect.com/science/article/pii/S0195669816300877