Let $ R $ be a commutative ring with identity and $\mathbb {A}(R) $ be the set of ideals of $
R $ with non-zero annihilators. In this paper, we first introduce and investigate the principal …

Let R be a commutative ring with identity and A*(R) be the set of non-zero ideals with non-
zero annihilators. The annihilatingideal graph of R is defined as the graph AG (R) with the …

Let R be a commutative ring with identity and 𝔸 (R) be the set of ideals of R with nonzero
annihilator. The annihilator-ideal graph of R, denoted by AI (R), is a simple graph with the …

Let R be a commutative ring with A⁢(R) its set of annihilating-ideals. The extended
annihilating-ideal graph of R, denoted by AG¯⁢(R), is an undirected graph with vertex set …

Let R be a commutative ring with identity. An ideal I of a ring R is called an annihilating-ideal
if there exists a nonzero ideal J of R such that IJ=(0) and we use the notation A (R) for the set …

For a commutative ring R with identity, the annihilating-ideal graph of R, denoted 𝔸𝔾 (R), is
the graph whose vertices are the nonzero annihilating ideals of R with two distinct vertices …

Let R be a commutative ring with identity and A∗(R) be the set of non-zero ideals with non-
zero annihilators. The annihilating-ideal graph of R is defined as the graph AG (R) with the …

Let R be a commutative ring with unity. The extension of annihilating-ideal graph of R,
$^{\bar {\mathbb {AG}}} $(R), is the graph whose vertices are nonzero annihilating ideals of …

Let R be a commutative ring with nonzero identity and I be a proper ideal of R. The
annihilator graph of R with respect to I, which is denoted by AG_ {I}(R), is the undirected …

Let R be a commutative ring with unity. The annihilator ideal graph of R, denoted by ΓAnn
(R), is a graph whose vertices are all non-trivial ideals of R and two distinct vertices I and J …