On spectral radii of unraveled balls

@article{Jiang2019OnSR,
  title={On spectral radii of unraveled balls},
  author={Zilin Jiang},
  journal={J. Comb. Theory, Ser. B},
  year={2019},
  volume={136},
  pages={72-80}
}
  • Zilin Jiang
  • Published 2019
  • Computer Science, Mathematics, Physics
  • J. Comb. Theory, Ser. B
  • 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 2 d − 1 cos ⁡ ( π r + 1 ) . 

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