Some Properties of Unitary Cayley Graphs

  • Walter Klotz
  • Torsten Sander

Abstract

The unitary Cayley graph $X_n$ has vertex set $Z_n=\{0,1, \ldots ,n-1\}$. 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.

Published
2007-06-21
Article Number
R45