Genre
Pre-printDate
2018-10-02Author
Richey, JShutty, N
Stover, M
Permanent link to this record
http://hdl.handle.net/20.500.12613/4908
Metadata
Show full item recordDOI
10.1080/10586458.2017.1311813Abstract
© 2018, © 2018 Taylor & Francis. The purpose of this article is to give explicit methods for bounding the number of vertices of finite k-regular graphs with given second eigenvalue. Let X be a finite k-regular graph and μ1(X) the second largest eigenvalue of its adjacency matrix. It follows from the well-known Alon–Boppana theorem that for any ε > 0 there are only finitely many such X with μ1(X) < (2 − ϵ)√k − 1, and we effectively implement Serre's quantitative version of this result. For any k and ε, this gives an explicit upper bound on the number of vertices in a k-regular graph with μ1(X) < (2 − ϵ)√k − 1).Citation to related work
Informa UK LimitedHas part
Experimental MathematicsADA compliance
For Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.eduae974a485f413a2113503eed53cd6c53
http://dx.doi.org/10.34944/dspace/4890