# Mathematical Models for Transport in Macroscopic and Mesoscopic Systems - Abstract

**Post, Olaf**

*Generalised discrete Laplacians and quantum graphs*

In this talk, we define a generalisation of the discrete Laplace operator on a combinatorial graph. These generalised Laplacians appear in a natural way from the spectral analysis of quantum graph Laplacians with general vertex boundary conditions. In the case of the standard (“Kirchhoff”) boundary conditions, the discrete operator is the usual combinatorial Laplacian. We also comment on trace formulas.