# 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} }

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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