Let $ R $ be a commutative ring with non-zero identity. The annihilator-inclusion ideal graph
of $ R $, denoted by $\xi_R $, is a graph whose vertex set is the of all non-zero proper ideals …

The rings considered in this paper are commutative with identity which are not integral
domains. Let R be a ring. Let us denote the set of all annihilating ideals of R by 𝔸 (R) and 𝔸 …

Let R be a commutative ring with non-zero 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). Let A (R) …

Let R be a commutative ring with nonzero identity. In this paper we intro-duce the
coannihilator graph of R, which is a dual of the annihilator graph AG (R), denoted by AG'(R) …

Let R be a commutative ring with identity and Z (R)∗ be the set of all nonzero zero-divisors
of R. The annihilator graph of commutative ring R is the simple undirected graph AG (R) with …

Throughout this dissertation, all rings are assumed to be a commutative ring with unity. In the
literature, there are many papers on assigning a graph to a ring, a group, semigroup or a …

Let R be a commutative ring with identity. The intersection graph of ideals of a ring R is an
undirected simple graph denoted by Γ (R) whose vertices are in a one-to-one …

Let $ R $ be a commutative ring with nonzero identity. The annihilator graph of $ R $,
denoted by $ AG (R) $, is the (undirected) graph whose vertex set is the set of all nonzero …

Let R be a commutative ring with Nil (R) its ideal of nilpotent elements, Z (R) its set of zero-
divisors, and Reg (R) its set of regular elements. In this paper, we introduce and investigate …