Domination polynomial of co-maximal graphs of integer modulo ring

We investigate the domination polynomial of the co-maximal graph $\mathrm{\Gamma }({\mathbb{Z}}_n)$ related to the ring of integers modulo $n$. Explicit formulas are derived for $n=p^{n_1}$ and $n=p^{n_1}{q}^{n_2}$, demonstrating that the resulting polynomials exhibit unimodality and log-concavity. For general $n$, we present structural expressions that connect $D(\mathrm{\Gamma }({\mathbb{Z}}_n),x)$ to appropriate induced subgraphs. Finally, we examine domination roots and establish bounds for their moduli using the Eneström–Kakeya theorem.