TY - JOUR

T1 - On spectral radii of unraveled balls

AU - Jiang, Zilin

N1 - Funding Information:
The work was done when the author was a postdoctoral fellow at Technion – Israel Institute of Technology, and was supported in part by ISF grant Nos. 1162/15, 936/16.
Funding Information:
The work was done when the author was a postdoctoral fellow at Technion ? Israel Institute of Technology, and was supported in part by ISF grant Nos. 1162/15, 936/16.
Publisher Copyright:
© 2018 Elsevier Inc.

PY - 2019/5

Y1 - 2019/5

N2 - 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]).

AB - 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]).

KW - Second largest eigenvalue

KW - Spectral radius

KW - The Alon–Boppana bound

KW - Universal cover

UR - http://www.scopus.com/inward/record.url?scp=85053718747&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053718747&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2018.09.003

DO - 10.1016/j.jctb.2018.09.003

M3 - Article

AN - SCOPUS:85053718747

VL - 136

SP - 72

EP - 80

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

ER -