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# Spectral analysis of metric graphs with infinite rays

### Abstract

We conduct a detailed analysis for finite metric graphs that have a semi-infinite chain (a ray) attached to each vertex. We show that the adjacency matrix of such a graph gives rise to a selfadjoint operator that is unitary equivalent to a direct sum of a finite number of simplest Jacobi matrices. This permitted to describe spectrums of such operators and to explicitly construct an eigenvector decomposition.

Key words: Metric graphs, adjacency matrix, Jacobi matrix, spectral analysis

### Article Information

 Title Spectral analysis of metric graphs with infinite rays Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 4, 391-396 MathSciNet MR3309675 zbMATH 1324.05118 Milestones Received 05/06/2014 Copyright The Author(s) 2014 (CC BY-SA)

### Authors Information

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

### Citation Example

L. P. Nizhnik, Spectral analysis of metric graphs with infinite rays, Methods Funct. Anal. Topology 20 (2014), no. 4, 391-396.

### BibTex

@article {MFAT751,
AUTHOR = {Nizhnik, L. P.},
TITLE = {Spectral analysis of metric graphs with infinite rays},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {4},
PAGES = {391-396},
ISSN = {1029-3531},
MRNUMBER = {MR3309675},
ZBLNUMBER = {1324.05118},
URL = {http://mfat.imath.kiev.ua/article/?id=751},
}