Polynomials of Unitary Cayley Graphs

The unitary Cayley graph $X_n$ has the vertex set $Z_n = \{0, 1, 2, \ldots, n - 1\}$ and vertices $a$ and $b$ are adjacent, if and only if $\gcd(a-b,n)=1$. In this paper, we present some properties of the clique, independence and distance polynomials of the unitary Cayley graphs and generalize some of the results from [W. Klotz, T. Sander, \textit{Some properties of unitary Cayley graphs}, Electr. J. Comb. 14 (2007), \#R45]. In addition, using some properties of Laplacian polynomial we determine the number of minimal spanning tress of any unitary Cayley graph.