Let R be a commutative ring with identity. The set 𝕀 (R) of all ideals of R is a bounded
semiring with respect to ordinary addition, multiplication and inclusion of ideals. The zero …

For a commutative ring with identity. Let AG (R) be the set of ideals of R with non-zero
annihilators. The annihilating-ideal graph of R with vertex set AG (R)*= AG (R)-{0} and two …

Let S be a commutative ring with unity, and a set of nonunit elements is denoted by WS. The
coannihilator graph of S, denoted by AG′ S, is an undirected graph with vertex set WS∗(set …

Let R be a commutative ring with identity which is not an integral domain. Let A (R)∗ denote
the collection of all nonzero annihilating ideals of R and AG (R) denote the annihilating ideal …

Let R be a commutative ring with identity. The essential ideal graph of R, denoted by ℰ R, is
a graph whose vertex set is the set of all nonzero proper ideals of R and two vertices I and J …

In this paper we introduce a new kind of graph associated with a commutative ring with
identity, and we discover some of its characterizations and properties. Let R be a …

Let R be a commutative ring with identity. The co-annihilating-ideal graph of R, denoted by
AR, is a graph whose vertex set is the set of all nonzero proper ideals of R and two distinct …

Rings considered in this article are commutative with identity which admit at least one
nonzero annihilating ideal. For such a ring R, we determine necessary and sufficient …

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. Recall that an ideal I of a ring R is called an annihilating ideal if there exists r∈ …