Two-Vertex Generators of Jacobians of Graphs

David Brandfonbrener, Pat Devlin, Netanel Friedenberg, Yuxuan Ke, Steffen Marcus, Henry Reichard, Ethan Sciamma

Abstract


We give necessary and sufficient conditions under which the Jacobian of a graph is generated by a divisor that is the difference of two vertices. This answers a question posed by Becker and Glass and allows us to prove various other propositions about the order of divisors that are the difference of two vertices. We conclude with some conjectures about these divisors on random graphs and support them with empirical evidence.


Keywords


Sandpile Groups; Critical Groups; Jacobians of Graphs

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