2017
Том 69
№ 6

All Issues

Spectral Analysis of Some Graphs with Infinite Rays

Lebid’ V. O., Nizhnik L. P.


Abstract

We perform a detailed spectral analysis of countable graphs formed by joining semibounded infinite chains to vertices of a finite graph. The spectrum of a self-adjoint operator generated by the adjacency matrix of the graph is characterized, the spectral measure is constructed, the eigenvectors are presented in the explicit form, and the spectral expansion in eigenvectors is obtained.

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 9, pp 1333-1345.

Citation Example: Lebid’ V. O., Nizhnik L. P. Spectral Analysis of Some Graphs with Infinite Rays // Ukr. Mat. Zh. - 2014. - 66, № 9. - pp. 1193–1204.