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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.

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