The comaximal graph $ Γ(R) $ of a commutative ring $R$ is a simple graph with vertex set $ R $ and two distinct vertices $ a $ and $b $ of $ Γ(R) $ are adjacent if and only if $ aR+bR=R $, where $ aR $ is the ideal generated by $ a $ in $ R $. In this article, the independent domination polynomial $ D_{i}(Γ(\mathbb{Z}_{n}),x) $ of $ Γ(\mathbb{Z}_{n}) $ is discussed, along with its unimodal and log-concave properties for certain values of $n$. Some auxiliary results related to $D_{i}(Γ(\mathbb{Z}_{n}),x)$ are presented in terms of their zeros. In addition, we determine the independence polynomial $ I(Γ(\mathbb{Z}_{n}),x ) $ of $ Γ(\mathbb{Z}_{n}) $ for special values of $n$ and provide a general result associated with it. The bounds for the zero of the polynomial $ I(Γ(\mathbb{Z}_{n}),x ) $ are established, and their log-concave and unimodal properties are examined.

翻译：交换环$R$的comaximal图$Γ(R)$是一个以$R$为顶点集的简单图，其中两个不同顶点$a$与$b$在$Γ(R)$中相邻当且仅当$aR+bR=R$，这里$aR$是由$a$在$R$中生成的理想。本文讨论了$Γ(\mathbb{Z}_{n})$的独立支配多项式$D_{i}(Γ(\mathbb{Z}_{n}),x)$，并研究了其对于某些$n$值的单峰性和对数凹性。基于多项式的零点，给出了与$D_{i}(Γ(\mathbb{Z}_{n}),x)$相关的一些辅助结论。此外，对于特定的$n$值，我们确定了$Γ(\mathbb{Z}_{n})$的独立多项式$I(Γ(\mathbb{Z}_{n}),x)$，并给出了与之相关的一般性结果。建立了多项式$I(Γ(\mathbb{Z}_{n}),x)$零点的界，并检验了其对数凹性和单峰性。