Open Access

# On new inverse spectral problems for weighted graphs

### Abstract

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.

Key words: Inverse spectral problem, weighted graph, spanning tree, adjacency matrix, index of a graph, spectrum of a graph, nonnegative matrix.

### Article Information

 Title On new inverse spectral problems for weighted graphs Source Methods Funct. Anal. Topology, Vol. 23 (2017), no. 1, 66-75 MathSciNet MR3632390 zbMATH 06810669 Milestones Received 23/10/2016 Copyright The Author(s) 2017 (CC BY-SA)

### Authors Information

L. P. Nizhnik
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

V. I. Rabanovich
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

### Citation Example

L. P. Nizhnik and V. I. Rabanovich, On new inverse spectral problems for weighted graphs, Methods Funct. Anal. Topology 23 (2017), no. 1, 66-75.

### BibTex

@article {MFAT924,
AUTHOR = {Nizhnik, L. P. and Rabanovich, V. I.},
TITLE = {On new inverse spectral problems for weighted graphs},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {23},
YEAR = {2017},
NUMBER = {1},
PAGES = {66-75},
ISSN = {1029-3531},
MRNUMBER = {MR3632390},
ZBLNUMBER = {06810669},
URL = {http://mfat.imath.kiev.ua/article/?id=924},
}

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