Document Zbl 1324.05118

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Nizhnik, L. P.

Spectral analysis of metric graphs with infinite rays. (English) Zbl 1324.05118

Methods Funct. Anal. Topol. 20, No. 4, 391-396 (2014).

The author gives a detailed analysis of spectral properties of infinite graphs consisting of a finite metric graph and a semi-infinite chain (a ray) attached to each vertex. It is shown that the adjacency matrix of such a graph defines a selfadjoint operator unitarily equivalent to a direct sum of a finite number of explicitly written Jacoby matrices. For several examples, spectra and eigenvectors are calculated.

Reviewer: Anatoly N. Kochubei (Kyïv)

Cited in 3 Documents

MSC:

05C50	Graphs and linear algebra (matrices, eigenvalues, etc.)
05C63	Infinite graphs
47B36	Jacobi (tridiagonal) operators (matrices) and generalizations

Keywords:

metric graph; adjacency matrix; Jacoby matrix

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