Graph de Rham Cohomology and the Automorphsim Group

Abstract

We introduce a graph-theoretical interpretation of an induced action of Aut$(\Gamma )$ in the discrete de Rham cohomology of a finite graph $\Gamma$. This action produces a splitting of Aut$(\Gamma )$ that depends on the cycles of $\Gamma$. We also prove some graph-theoretical analogues of standard results in differential geometry, in particular, a graph version of Stokes' Theorem and the Mayer-Vietoris sequence in cohomology.

15 pages, 4 figures, version 2

References in corpus (3)

• Discrete path integral approach to the trace formula for regular graphs
• The Graph Laplacian and Morse Inequalities
• Graph Automorphisms from the Geometric Viewpoint