An Ambarzumian type theorem on graphs with odd cycles

Abstract

We consider an inverse problem for Schrödinger operators on a connected equilateral graph $G$ with standard matching conditions. The graph $G$ consists of at least two odd cycles glued together at a common vertex. We prove an Ambarzumian type result, i.e., if a specific part of the spectrum is the same as in the case of zero potential, then the potential has to be zero.

arXiv admin note: text overlap with arXiv:1610.00971