Independent Domination Polynomial of Comaximal Graphs of Commutative Rings

The comaximal graph [Formula: see text] of a commutative ring [Formula: see text] is a simple graph with vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] of [Formula: see text] adjacent if and only if [Formula: see text], where [Formula: see text] is the ideal generated by [Formula: see text] in [Formula: see text]. In this article, the independent domination polynomial [Formula: see text] of [Formula: see text] is discussed, along with its unimodal and log-concave properties for certain values of [Formula: see text]. Some auxiliary results related to [Formula: see text] are presented in terms of their zeros. In addition, we determine the independence polynomial [Formula: see text] of [Formula: see text] for special values of [Formula: see text] and provide a general result associated with it. The bounds for the zeros of the polynomial [Formula: see text] are established, and its log-concave and unimodal properties are examined.