Klotz, Walter; Sander, Torsten Some properties of unitary Cayley graphs. (English) Zbl 1121.05059 Electron. J. Comb. 14, No. 1, Research paper R45, 12 p. (2007). Summary: The unitary Cayley graph \(X_n\) has vertex set \(Z_n=\{0,1, \dots ,n-1\}\). Vertices \(a,~b\) are adjacent, if gcd\((a-b,n)=1\). For \(X_n\), the chromatic number, the clique number, the independence number, the diameter and the vertex connectivity are determined. We decide on the perfectness of \(X_n\) and show that all nonzero eigenvalues of \(X_n\) are integers dividing the value \(\varphi(n)\) of the Euler function. Cited in 4 ReviewsCited in 70 Documents MSC: 05C25 Graphs and abstract algebra (groups, rings, fields, etc.) 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.) Keywords:chromatic number; clique number; independence number; diameter; connectivity PDFBibTeX XMLCite \textit{W. Klotz} and \textit{T. Sander}, Electron. J. Comb. 14, No. 1, Research paper R45, 12 p. (2007; Zbl 1121.05059) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Number of positive integers, k, where k <= n and gcd(k,n) = gcd(k+1,n) = 1. Number of positive integers, k, where k <= 2n+1 and gcd(k, 2n+1) = gcd(k+1, 2n+1) = 1.