An Ambarzumian type theorem on graphs with odd cycles

Abstract

UDC 517.9 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 must be equal to zero.