Note on the girth of Ramanujan graphs
A Ramanujan graph in a finite k-regular graph all eigenvalues of which, other than \(\pm k\), have modulus at most \(2\sqrt{k-1}\). Such graphs are well-suited for the construction of expanders. \textit{A. Lubotzky, R. Phillips} and \textit{P. Sarnak} [Combinatorica 8, No.3, 261-277 (1988; Zbl 0661.05035)] presented, for infinitely many k, an explicit construction of such graphs with order n and girth g asymptotically satisfying \((\log_{k-1}n)/g\leq 3/4\). The author shows this bound to be sharp.
scientific article; zbMATH DE number 4162912