On spectral radii of unraveled balls

Zilin Jiang

doi:10.1016/j.jctb.2018.09.003

On spectral radii of unraveled balls

Zilin Jiang

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Given a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We prove a lower bound on the maximum spectral radius of unraveled balls of fixed radius, and we show, among other things, that if the average degree of G after deleting any ball of radius r is at least d then its second largest eigenvalue is at least 2d−1cos⁡([Formula presented]).

Original language	English (US)
Pages (from-to)	72-80
Number of pages	9
Journal	Journal of Combinatorial Theory. Series B
Volume	136
DOIs	https://doi.org/10.1016/j.jctb.2018.09.003
State	Published - May 2019
Externally published	Yes

Keywords

Second largest eigenvalue
Spectral radius
The Alon–Boppana bound
Universal cover

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jctb.2018.09.003

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abstract = "Given a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We prove a lower bound on the maximum spectral radius of unraveled balls of fixed radius, and we show, among other things, that if the average degree of G after deleting any ball of radius r is at least d then its second largest eigenvalue is at least 2d−1cos⁡([Formula presented]).",

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doi = "10.1016/j.jctb.2018.09.003",

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AB - Given a graph G, the unraveled ball of radius r centered at a vertex v is the ball of radius r centered at v in the universal cover of G. We prove a lower bound on the maximum spectral radius of unraveled balls of fixed radius, and we show, among other things, that if the average degree of G after deleting any ball of radius r is at least d then its second largest eigenvalue is at least 2d−1cos⁡([Formula presented]).

KW - Second largest eigenvalue

KW - Spectral radius

KW - The Alon–Boppana bound

KW - Universal cover

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JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

On spectral radii of unraveled balls

Abstract

Keywords

ASJC Scopus subject areas

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