  We consider Laplace operators on metric graphs, networks of one-dimensional
line segments (bonds), with matching conditions at the vertices that make the
operator self-adjoint. Such quantum graphs provide a simple model of quantum
mechanics in a classically chaotic system with multiple scales corresponding to
the lengths of the bonds. For graph Laplacians we briefly report results for
the spectral determinant, vacuum energy and heat kernel asymptotics of general
graphs in terms of the vertex matching conditions.
