Leaf-response measurements on a tree of elastic strings determine the strings' lengths and speeds, the branching pattern, and the angles at the joints, under generic non-degenerate conditions.
Belishev, Boundary spectral inverse problem on a class of graphs (tree s) by the BC method, Inverse Problems 20 (2004), 647–672
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On an inverse problem for tree-like networks of elastic strings
Leaf-response measurements on a tree of elastic strings determine the strings' lengths and speeds, the branching pattern, and the angles at the joints, under generic non-degenerate conditions.