Independent Domination Polynomial of Comaximal Graphs of Commutative Rings
摘要
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)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 Di(Γ(Zn),x)of Γ(Zn)is discussed,along with its unimodal and log-concave properties for certain values of n.Some auxiliary results related to Di(Γ(Zn),x)are presented in terms of their zeros.In addition,we determine the independence polynomial I(Γ(Zn),x)of Γ(Zn)for special values of n and provide a general result associated with it.The bounds for the zeros of the polynomial I(Γ(Zn),x)are established,and its log-concave and unimodal properties are examined.
年，卷(期)：
2026, 33(2)
分类号：
05C31
05C25
05C69
12D10
机标分类号：
TP13
TP301.6
O141.3
在线出版日期：
2026年7月17日
