Face-vertex incidence matrices of arbitrary graphs generate exactly flat bands with degeneracy at least the number of faces minus the number of vertices.
The theorems of Green-Stokes,Gauss-Bonnet and Poincare-Hopf in Graph Theory
1 Pith paper cite this work, alongside 9 external citations. Polarity classification is still indexing.
1
Pith paper citing it
9
external citations · Pith
abstract
By proving graph theoretical versions of Green-Stokes, Gauss-Bonnet and Poincare-Hopf, core ideas of undergraduate mathematics can be illustrated in a simple graph theoretical setting. In this pedagogical exposition we present the main proofs on a single page and add illustrations. While discrete Stokes is is old, the other two results for graphs were found only recently.
fields
cond-mat.str-el 1years
2026 1verdicts
CONDITIONAL 1representative citing papers
citing papers explorer
-
New class of exactly flat topological bands - compact localised states protected by local graph topology
Face-vertex incidence matrices of arbitrary graphs generate exactly flat bands with degeneracy at least the number of faces minus the number of vertices.