Inverse problems on a graph with loops

Abstract

AbstractA graph with loops, endowed with standard matching conditions in the internal vertex and with Dirichlet boundary conditions at the boundary vertices, is considered. We show that the potential on a graph with loops can be constructed by the dense nodal points on the interval considered. Moreover, we investigate the so-called incomplete inverse problems of recovering the potential on a fixed edge from a subset of nodal points situated only on a part of the edge.