*Article* **An Inverse Problem for Quantum Trees with Delta-Prime Vertex Conditions**

**Sergei Avdonin 1,2,† and Julian Edward 3,\*,†**


Received: 30 September 2020; Accepted: 16 November 2020; Published: 17 November 2020 -

**Abstract:** In this paper, we consider a non-standard dynamical inverse problem for the wave equation on a metric tree graph. We assume that the so-called delta-prime matching conditions are satisfied at the internal vertices of the graph. Another specific feature of our investigation is that we use only one boundary actuator and one boundary sensor, all other observations being internal. Using the Neumann-to-Dirichlet map (acting from one boundary vertex to one boundary and all internal vertices) we recover the topology and geometry of the graph together with the coefficients of the equations.

**Keywords:** inverse problems; quantum graphs; delta-prime vertex conditions
