A classification of Ramanujan unitary Cayley graphs
Summary: The unitary Cayley graph on \(n\) vertices, \(X_n\), has vertex set \(\frac{\mathbb Z}{n\mathbb Z}\) and two vertices \(a\) and \(b\) are connected by an edge if and only if they differ by a multiplicative unit modulo \(n\), i.e. gcd\((a-b,n)=1\). A \(k\)-regular graph \(X\) is Ramanujan if and only if \(\lambda(X)\leq 2\sqrt{k-1}\) where \(\lambda(X)\) is the second largest absolute value of the eigenvalues of the adjacency matrix of \(X\). We obtain a complete characterization of the cases in which the unitary Cayley graph \(X_n\) is a Ramanujan graph.
scientific article; zbMATH DE number 5721438