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.