The theorems of Green-Stokes,Gauss-Bonnet and Poincare-Hopf in Graph Theory

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.

arXiv comment10 pages, 30 figures, pedagogical exposition

References in corpus (2)

• A graph theoretical Gauss-Bonnet-Chern Theorem
• A graph theoretical Poincare-Hopf Theorem

Cited by in corpus (9)

• The Dirac operator of a graph
• Gauss-Bonnet for multi-linear valuations
• Coloring graphs using topology
• A notion of graph homeomorphism
• Classical mathematical structures within topological graph theory
• The amazing world of simplicial complexes
• The Jordan-Brouwer theorem for graphs
• Poincare Hopf for vector fields on graphs
• If Archimedes would have known functions