Some properties of unitary Cayley graphs

Abstract

The unitary Cayley graph Xn has vertex set Zn = {0,1, . . .,n-1}. Vertices a, b are adjacent, if gcd(a - b, n) = 1. For Xn the chromatic number, the clique number, the independence number, the diameter and the vertex connectivity are determined. We decide on the perfectness of Xn and show that all nonzero eigenvalues of Xn are integers dividing the value φ(n) of the Euler function.