On new inverse spectral problems for weighted graphs - Nizhnik, L. P.; Rabanovich, V. I. (Methods of Functional Analysis and Topology, 2017)
In this paper, we consider various new inverse spectral problems (ISP) for metric graphs, using maximal eigen values of the adjacency matrix of the graph and its subgraphs as well as the corresponding eigen vectors or some of their components as spectral data. We give examples of spectral data that uniquely determine the metric on the graph. Effective algorithms for solving the considered ISP are given.