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Gluing of
graphs and their Jacobians
Alessandro Chilelli and Jaiung Jun |
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Vol. 16 (2023), No. 3, 389–407
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Abstract |
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The Jacobian of a graph is a discrete analogue of the Jacobian of a Riemann surface. We explore how Jacobians of graphs change when we glue two graphs along a common subgraph focusing on the case of cycle graphs. Then, we link the computation of Jacobians of graphs with cycle matrices. Finally, we prove that Tutte’s rotor construction with his original example produces two graphs with isomorphic Jacobians when all involved graphs are planar. This answers the question posed by Clancy, Leake, and Payne (Exp. Math. 24:1 (2015), 1–7), stating it is affirmative in this case. |
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Keywords
Jacobian of a graph, sandpile group, critical group,
chip-firing game, gluing graphs, cycle graph, Tutte
polynomial, Tutte's rotor construction
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Mathematical Subject Classification
Primary: 05C50, 05C76
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Milestones
Received: 21 March 2021
Revised: 9 March 2022
Accepted: 13 June 2022
Published: 10 August 2023
Communicated by Kenneth S. Berenhaut
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Authors |
| Alessandro Chilelli | |
| Department of Mathematics State University of New York at Albany Albany, NY United States |
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| Jaiung Jun | |
| Department of Mathematics State University of New York at New Paltz New Paltz, NY United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
