The present book deals with the spectral geometry of infinite graphs. This topic involves the
interplay of three different subjects: geometry, the spectral theory of Laplacians and the heat …

We study Laplacians on graphs and networks via regular Dirichlet forms. We give a sufficient
geometric condition for essential selfadjointness and explicitly determine the generators of …

We study the uniqueness of self-adjoint and Markovian extensions of the Laplacian on
weighted graphs. We first show that, for locally finite graphs and a certain family of metrics …

We study Laplacians associated to a graph and single out a class of such operators with
special regularity properties. In the case of locally finite graphs, this class consists of all …

We present a study of what may be called an intrinsic metric for a general regular Dirichlet
form. For such forms we then prove a Rademacher type theorem. For strongly local forms we …

For a given subcritical discrete Schrödinger operator H on a weighted infinite graph X, we
construct a Hardy-weight w which is optimal in the following sense. The operator H− λ w is …

We study solutions of the generalized porous medium equation on infinite graphs. For
nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild …

We study energy functionals associated with quasi-linear Schrödinger operators on infinite
weighted graphs, and develop a ground state representation. Using the representation, we …

Essential Self-adjointness for Combinatorial Schrödinger Operators II-Metrically non Complete
Graphs Page 1 Math Phys Anal Geom (2011) 14:21–38 DOI 10.1007/s11040-010-9086-7 …

We study the connections between volume growth, spectral properties and stochastic
completeness of locally finite weighted graphs. For a class of graphs with a very weak …