Cospectral quantum graphs in the case of Dirichlet conditions at pendant vertices
Abstract
UDC 517.9
We consider spectral problems generated by the Sturm–Liouville equation on connected simple equilateral graphs with Neumann and Dirichlet boundary conditions at the pendant vertices and the conditions of continuity and Kirchhoff's conditions at the inner vertices. We describe the cases where the first and the second terms of the asymptotics of eigenvalues uniquely determine the shape either of the graph or of its interior subgraph.
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