Nodal geometry of graphs on surfaces

Yong Lin*, Gábor Lippner, Dan Mangoubi, Shing Tung Yau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We prove two mixed versions of the Discrete Nodal Theorem of Davies et. al. [3] for bounded degree graphs, and for three-connected graphs of fixed genus g. Using this we can show that for a three-connected graph satisfying a certain volume-growth condition, the multiplicity of the nth Laplacian eigenvalue is at most 2 [6(n - 1) + 15(2g - 2)]2. Our results hold for any Schrodinger operator, not just the Laplacian.

Original languageAmerican English
Pages (from-to)1291-1298
Number of pages8
JournalDiscrete and Continuous Dynamical Systems
Issue number3
StatePublished - Nov 2010


  • Genus
  • Multiplicity of eigenvalues
  • Nodal domain


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