Download this article
Download this article For screen
For printing
Recent Issues
Volume 18
Volume 16
Volume 15
Volume 14
Volume 13
Volume 12
Volume 11
Volume 10
Volume 9
Volume 8
Volume 6+7
Volume 5
Volume 4
Volume 3
Volume 2
Volume 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN (electronic): 2640-7345
ISSN (print): 2640-7337
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Critical groups of strongly regular graphs and their generalizations

Kenneth Hung and Chi Ho Yuen

Vol. 19 (2022), No. 3, 95–109

We determine the maximum order of an element in the critical group of a strongly regular graph, and show that it achieves the spectral bound due to Lorenzini. We extend the result to all graphs with exactly two nonzero Laplacian eigenvalues, and study the signed graph version of the problem. We also study the monodromy pairing on the critical groups, and suggest an approach to study the structure of these groups using the pairing.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

critical group, sandpile group, Jacobian, strongly regular graph, signed graph, graph Laplacian, monodromy pairing
Mathematical Subject Classification
Primary: 05C50
Secondary: 05C22, 05E30, 14H40
Received: 29 December 2021
Revised: 26 April 2022
Accepted: 23 May 2022
Published: 25 July 2022
Kenneth Hung
San Francisco, CA 94105
United States
Chi Ho Yuen
Department of Mathematics
University of Oslo
0851 Oslo