On new inverse spectral problems for weighted graphs
DOI:
Keywords:
Inverse spectral problem, weighted graph, spanning tree, adjacency matrix, index of a graph, spectrum of a graph, nonnegative matrixAbstract
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.References
M. T. Chu, Inverse eigenvalue problems, SIAM Rev. 40 (1998), no. 1, 1-39. MathSciNet CrossRef
M. T. Chu and G. H. Golub, Structured inverse eigenvalue problems, Acta Numer. 11 (2002), 1-71. MathSciNet CrossRef
S. Friedland, Inverse eigenvalue problems, Linear Algebra and Appl. 17 (1977), no. 1, 15-51. MathSciNet
F. P. Gantmacher and M. G. Krein, Oscillation matrices and kernels and small vibrations of mechanical systems, AMS Chelsea Publishing, Providence, RI, 2002. MathSciNet CrossRef
F. R. Gantmakher, Teoriya matrits (Theory of matrices), Fizmatlit, Moscow, 2004 (Russian).
H. Hochstadt, On the construction of a Jacobi matrix from mixed given data, Linear Algebra Appl. 28 (1979), 113-115. MathSciNet CrossRef
L. Hogben (ed.), Handbook of linear algebra, CRC Press, Boca Raton, FL, 2014. MathSciNet
