Realization of groups with pairing as jacobians of finite graphs

Louis Gaudet, David Jensen, Dhruv Ranganathan, Nicholas Wawrykow, Theodore Weisman

Research output: Contribution to journalArticlepeer-review


We study which groups with pairing can occur as the Jacobian of a finite graph. We provide explicit constructions of graphs whose Jacobian realizes a large fraction of odd groups with a given pairing. Conditional on the generalized Riemann hypothesis, these constructions yield all groups with pairing of odd order, and unconditionally, they yield all groups with pairing whose prime factors are sufficiently large. For groups with pairing of even order, we provide a partial answer to this question, for a certain restricted class of pairings. Finally, we explore which finite abelian groups occur as the Jacobian of a simple graph. There exist infinite families of finite abelian groups that do not occur as the Jacobians of simple graphs.

Original languageEnglish
Pages (from-to)781-801
Number of pages21
JournalAnnals of Combinatorics
Issue number4
StatePublished - Jan 1 2018

Bibliographical note

Publisher Copyright:
© 2018 Springer Nature Switzerland AG.


  • Graph jacobians
  • Groups with pairing

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Realization of groups with pairing as jacobians of finite graphs'. Together they form a unique fingerprint.

Cite this