# Some properties and domination number of the complement of a new graph associated to a commutative ring

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### "Some properties and domination numb..." refers background or methods in this paper

...The annihilatingideal graph of a commutative ring and other related graphs have been studied by several researchers (see for example, [1, 2, 14, 18, 19])....

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...Several interesting and inspiring theorems were proved on ΩR in [2] (see for example, Theorems 4, 10, and 20)....

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...Motivated by the work done on the annihilating-ideal graph of a commutative ring, in [2], Alilou, Amjadi and Sheikholeslami introduced and studied a new graph associated to a commutative ring R, denoted by ΩR, which is an undirected graph whose vertex set is the set of all nontrivial ideals of 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) (that is, if and only if either AnnRI ⊆ AnnRJ or AnnRJ ⊆ AnnRI), where for an ideal I of R, the annihilator of I in R, denoted by AnnRI is defined as AnnRI = {r ∈ R : Ir = (0)}....

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