Geodesic
Two-vertex generators of Jacobians of graphs
David Brandfonbrener1 ; Pat Devlin1 ; Netanel Friedenberg1 ; Yuxuan Ke1 ; Steffen Marcus2 ; Henry Reichard1 ; Ethan Sciamma1
1Yale University
2The College of New Jersey
The electronic journal of combinatorics, Tome 25 (2018) no. 1
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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.
DOI : 10.37236/7302
Classification : 05C25, 05C50, 05C57, 05C80
Mots-clés : sandpile groups, critical groups, Jacobians of graphs

David Brandfonbrener  1   ; Pat Devlin  1   ; Netanel Friedenberg  1   ; Yuxuan Ke  1   ; Steffen Marcus  2   ; Henry Reichard  1   ; Ethan Sciamma  1

1 Yale University
2 The College of New Jersey 
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     title = {Two-vertex generators of {Jacobians} of graphs},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {1},
     doi = {10.37236/7302},
     zbl = {1380.05098},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/7302/}
}
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David Brandfonbrener; Pat Devlin; Netanel Friedenberg; Yuxuan Ke; Steffen Marcus; Henry Reichard; Ethan Sciamma. Two-vertex generators of Jacobians of graphs. The electronic journal of combinatorics, Tome 25 (2018) no. 1. doi: 10.37236/7302

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