Spectra of infinite graphs: two methods of computation
Combinatorics
2020-01-24 v1 Spectral Theory
Abstract
Two method for computation of the spectra of certain infinite graphs are suggested. The first one can be viewed as a reversed Gram--Schmidt orthogonalization procedure. It relies heavily on the spectral theory of Jacobi matrices. The second method is related to the Schur complement for block matrices. A number of examples including infinite graphs with tails, chains of cycles and ladders are worked out in detail.
Cite
@article{arxiv.2001.08596,
title = {Spectra of infinite graphs: two methods of computation},
author = {Leonid Golinskii},
journal= {arXiv preprint arXiv:2001.08596},
year = {2020}
}
Comments
43 pages, 13 figures