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
SN - 0095-8956
VL - 136
SP - 72
EP - 80
JO - Journal of Combinatorial Theory. Series B
JF - Journal of Combinatorial Theory. Series B
ER -