On spectral radii of unraveled balls

Research output: Contribution to journalArticlepeer-review

1 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 languageEnglish (US)
Pages (from-to)72-80
Number of pages9
JournalJournal of Combinatorial Theory. Series B
Volume136
DOIs
StatePublished - May 2019
Externally publishedYes

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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