Spectra of infinite graphs via Schur complement
L. Golinskii
TL;DR
This paper explores the use of the Schur complement operator technique to compute the spectra of infinite graphs formed by attaching rays to finite graphs, with examples including multiple star and flower graphs.
Contribution
It introduces a novel application of the Schur complement to analyze spectra of infinite graphs with attached rays, expanding spectral graph theory methods.
Findings
Successfully computed spectra for specific infinite graphs
Demonstrated the effectiveness of Schur complement in spectral analysis
Provided explicit spectral descriptions for star and flower graphs
Abstract
The goal of the paper is to apply the general operator theoretic construction known as the Schur complement for computation of the spectrum of certain infinite graphs which can be viewed as finite graphs with the ray attached to them. The examples of a multiple star and a flower with infinite rays are considered.
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Taxonomy
TopicsGraph theory and applications · Matrix Theory and Algorithms · Spectral Theory in Mathematical Physics