some results on the complement of a new graph associated to a commutative ring

The rings considered in this article are commutative with identity which admit at least one nonzero proper ideal. let r be a ring. we denote the collection of all ideals of r by i(r) and i(r){(0)} by i(r) ^∗. alilou et al. [a. alilou, j. amjadi and s.m. sheikholeslami, a new graph associated to a commutative ring, discrete math. algorithm. appl. 8 (2016) article id: 1650029 (13 pages)] introduced and investigated a new graph associated to r, denoted by ω^∗ r which is an undirected graph whose vertex set is i(r) ^∗{r} and distinct vertices i, j are joined by an edge in this graph if and only if either (annri)j = (0) or (annrj)i = (0). several interesting theorems were proved on ω^∗ r in the aforementioned paper and they illustrate the interplay between the graph-theoretic properties of ω^∗ r and the ring-theoretic properties of r. the aim of this article is to investigate some properties of (ω^∗ r) c , the complement of the new graph ω^∗ r associated to r.