Two-vertex generators of Jacobians of graphs

Two-vertex generators of Jacobians of graphs

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...

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Veröffentlicht in:arXiv.org 2017-09
Hauptverfasser: Brandfonbrener, David, Devlin, Pat, Friedenberg, Netanel, Yuxuan Ke, Marcus, Steffen, Reichard, Henry, Sciamma, Ethan
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Graphs
Jacobians
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Zusammenfassung: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.
ISSN:2331-8422