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.
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Klotz et al. (2007) studied this question.
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