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.
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