Tight estimates for eigenvalues of regular graphs
Summary: It is shown that if a \(d\)-regular graph contains \(s\) vertices so that the distance between any pair is at least \(4k\), then its adjacency matrix has at least \(s\) eigenvalues which are at least \(2\sqrt{d-1}\cos({\pi\over 2k})\). A similar result has been proved by Friedman using more sophisticated tools.
scientific article; zbMATH DE number 2107514