On high-girth expander graphs with localized eigenvectors
Shohei Satake
TL;DR
This paper constructs high-girth regular expander graphs with localized eigenvectors for various degrees, addressing a recent open problem and expanding understanding of eigenvector localization in graph theory.
Contribution
It introduces a method to construct high-girth regular expanders with localized eigenvectors for general degrees, advancing the theory of eigenvector localization in graphs.
Findings
Successfully constructed high-girth regular expanders with localized eigenvectors
Extended the class of degrees for which such graphs can be constructed
Provided insights into eigenvector localization phenomena in high-girth graphs
Abstract
The main purpose of this paper is to construct high-girth regular expander graphs with localized eigenvectors for general degrees, which is inspired by a recent work due to Alon, Ganguly and Srivastava (to appear in Israel J. Math.).
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Advanced Differential Equations and Dynamical Systems