### Abstract

We consider general self-adjoint realisations of the Laplacian on a compact metric graph and study their spectral properties. We prove a trace formula that expresses the spectral density in terms of a sum over periodic orbits on the graph.

## An Isaac Newton Institute Workshop## Quantum Graphs, their Spectra and Applications## Sectral properties and trace formulae for quantum graphs with general self-adjoint boundary conditions
## AbstractWe consider general self-adjoint realisations of the Laplacian on a compact metric graph and study their spectral properties. We prove a trace formula that expresses the spectral density in terms of a sum over periodic orbits on the graph. |