Independent domination polynomial for the cozero divisor graph of the ring of integers modulo n

The cozero divisor graph Γ (R) of a commutative ring R is a simple graph whose vertex set is the set of non-zero non-unit elements of R such that two distinct vertices x and y of Γ (R) are adjacent if and only if x / ∈ Ry and y / ∈ Rx, where Rx is the ideal generated by x. In this article, the independent domination polynomial of Γ (Zn) is found for n ∈ p1p2, p1p2p3, p n 1 1 p2, where pi's are primes, n1 is an integer greater than 1, and Zn is the integer modulo ring. It is shown that the independent domination polynomial of Γ (Zp 1 p 2) has only one real root. It is also proved that these polynomials are not unimodal but are log-concave under certain conditions.