  We consider an inverse problem for Schr\"odinger 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.

Spectral Theory