A classification of Ramanujan unitary Cayley graphs
type: Item
instance of: scholarly article
title: A classification of Ramanujan unitary Cayley graphs
zbMATH Open document ID: 1189.05147
author: Andrew Droll
published in: The Electronic Journal of Combinatorics
publication date: 2010-06-16T00:00:00Z
full work available at URL: https://eudml.org/doc/229152
full work available at URL: v17i1n29.html
review text: 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.
Mathematics Subject Classification ID: 05C75
zbMATH DE Number: 5721438
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5721438