The theorems of Green-Stokes,Gauss-Bonnet and Poincare-Hopf in Graph   Theory
  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. 
Oliver Knill
math.DG cs.DM