2 papers
math-ph2025
Non-existence of co-spectral simple connected graphs with small number of edges
O. Boyko, D. Kaliuzhnyi-Verbovetskyi, V. Pivovarchik
We prove that if the number of edges does not exceed 7 then the asymptotics of eigenvalues of the Dirichlet problem uniquely determine the shape of the graph.
math.FA2025
Recovering the shape of a quantum tree by scattering data
Olga Boyko, Yuri Latushkin, Vyacheslav Pivovarchik
We consider a scattering problem generated by the Sturm-Liouville equation on a tree which consists of an equilateral compact subtree and a half-infinite lead attached to its root.…