On spectral radii of unraveled balls
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 $2\sqrt{d-1}\cos(\frac{\pi}{r+1})$.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2017
- DOI:
- 10.48550/arXiv.1710.06719
- arXiv:
- arXiv:1710.06719
- Bibcode:
- 2017arXiv171006719J
- Keywords:
-
- Mathematics - Combinatorics;
- 05C50;
- 60J10;
- 15A42
- E-Print:
- 8 pages, accepted to J. Comb. Theory B, corrections suggested by the referees have been incorporated