### Polynomials of unitary Cayley graphs

#### Abstract

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.

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