Let R be a commutative ring. The annihilator graph of R, denoted by AG (R), is the
undirected graph with all nonzero zero-divisors of R as vertex set, and two distinct vertices x …

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

Let $ R $ be a commutative ring with identity, and $ mathrm {A}(R) $ be the set of ideals with
non-zero annihilator. The annihilating-ideal graph of $ R $ is defined as the graph $ AG (R) …

In this paper, we consider the intersection graph G (R) of nontrivial left ideals of a ring R. We
characterize the rings R for which the graph G (R) is connected and obtain several …

Let R be a commutative ring with identity which is not an integral domain. Let 𝔸 (R) denote
the set of all annihilating ideals of R and let us denote 𝔸 (R)\{(0)} by 𝔸 (R)∗. For an ideal I of …

Let be a commutative ring with identity, and let be the set of zero-divisors of. Anderson and
Badawi introduced the well-known total graph of, denoted by, as the graph with the vertex …

Let R be a commutative ring with unity 1≠ 0. The annihilating-ideal graph of R, denoted by
𝔸 𝔾 (R), is defined to be the graph with vertex set A∗(R)—the set of non-zero annihilating …

The inclusion ideal graph of a ring R, denoted by In (R), is a graph whose vertices are all
non-trivial left ideals of R and two distinct left ideals I and J are adjacent if and only if I⊆ J or …

Let R be a commutative ring with identity which is not an integral domain. An ideal I of a ring
R is called an annihilating ideal if there exists r∈ R\{0} such that Ir=(0). In this paper, we …

‎ The rings considered in this article are commutative with identity which admit at least two
maximal ideals‎.‎ This article is inspired by the work done on the comaximal ideal graph of a …