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Critical groups of
strongly regular graphs and their generalizations
Kenneth Hung and Chi Ho Yuen |
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Vol. 19 (2022), No. 3, 95–109
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Abstract |
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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. |
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Keywords
critical group, sandpile group, Jacobian, strongly regular
graph, signed graph, graph Laplacian, monodromy pairing
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Mathematical Subject Classification
Primary: 05C50
Secondary: 05C22, 05E30, 14H40
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Milestones
Received: 29 December 2021
Revised: 26 April 2022
Accepted: 23 May 2022
Published: 25 July 2022
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Authors |
| Kenneth Hung | |
| Meta San Francisco, CA 94105 United States |
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| Chi Ho Yuen | |
| Department of Mathematics University of Oslo 0851 Oslo Norway |
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