Some Properties of Unitary Cayley Graphs

Some Properties of Unitary Cayley Graphs

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 sh...

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Veröffentlicht in:The Electronic journal of combinatorics 2007-06, Vol.14 (1)
Hauptverfasser: Klotz, Walter, Sander, Torsten
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description 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.
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