An Ambarzumian type theorem on graphs with odd cycles

  • M. Kiss Inst. Math. Budapest Univ. Technology and Economics, Hungary
Keywords: Ambarzumian, inverse problems, inverse eigenvalue problem, differential equations on graphs, quantum graphs, Schrodinger operators, odd cycles


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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How to Cite
Kiss, M. “An Ambarzumian Type Theorem on Graphs With Odd Cycles”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, no. 12, Jan. 2023, pp. 1679 -85, doi:10.37863/umzh.v74i12.6734.
Research articles