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 $2\sqrt{d-1}\cos (\frac{\pi }{r+1})$.

8 pages, accepted to J. Comb. Theory B, corrections suggested by the referees have been incorporated

References in corpus (1)

• A strengthening and a multipartite generalization of the Alon-Boppana-Serre Theorem

Cited by in corpus (2)

• Forbidden subgraphs for graphs of bounded spectral radius, with applications to equiangular lines
• Alon-Boppana-type bounds for weighted graphs