A Calderón type inverse problem for tree graphs (Q2134551)

The authors consider the inverse problem of recovering a tree graph, including the weights on its edges, from the knowledge of the Dirichlet-to-Neumann matrix associated with the Laplacian. An explicit formula is given, relating this matrix to the pairwise weighted distances of the leaves of the tree. As a result, the related weighted tree is recovered. The main result can be viewed as a counterpart of the Calderon problem in the analysis of partial differential equations. It is worth to notice that a lot of work has already been done on the subject. Here, the novelty is that the considered inverse problem is solved under weaker assumptions.