We present a systematic collection of spectral surgery principles for the Laplacian on a
compact metric graph with any of the usual vertex conditions (natural, Dirichlet, or $\delta …

This open access book gives a systematic introduction into the spectral theory of differential
operators on metric graphs. Main focus is on the fundamental relations between the …

We consider the problem of finding universal bounds of “isoperimetric” or “isodiametric” type
on the spectral gap of the Laplacian on a metric graph with natural boundary conditions at …

We derive a number of upper and lower bounds for the first nontrivial eigenvalue of
Laplacians on combinatorial and quantum graph in terms of the edge connectivity, ie the …

A finite discrete graph is turned into a quantum (metric) graph once a finite length is
assigned to each edge and the one-dimensional Laplacian is taken to be the operator. We …

The plan for this book arose from the desire for an introductory text on spectral theory, which
would not assume functional analysis as a prerequisite. I wanted this text to include …

We consider the nonlinear Schrödinger equation with pure power nonlinearity on a general
compact metric graph, and in particular its stationary solutions with fixed mass. Since the the …

We propose a simple method for resolution of cospectrality of Schrödinger operators on
metric graphs. Our approach consists of attaching a lead to them and comparing the S …

We investigate the bottom of the spectra of infinite quantum graphs, ie, Laplace operators on
metric graphs having infinitely many edges and vertices. We introduce a new definition of …

In this paper we study Schrödinger operators with absolutely integrable potentials on metric
graphs. Uniform bounds—ie depending only on the graph and the potential—on the …