In this paper we continue our study of annihilating-ideal graph of commutative rings, that
was introduced in (The annihilating-ideal graph of commutative rings I, to appear in J …

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

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

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 …

Let R be a commutative ring with nonzero identity, Z (R) be its set of zero-divisors, and if a∈
Z (R), then let ann R (a)={d∈ R| da= 0}. The annihilator graph of R is the (undirected) graph …

Let R be a commutative ring. The total graph of R, denoted by T (Γ (R)) is a graph with all
elements of R as vertices, and two distinct vertices x, y∈ R, are adjacent if and only if x+ y∈ …

In this paper, a new kind of graph on a commutative ring R with identity, namely the co-
maximal ideal graph is defined and studied. We use to denote this graph, with its vertices the …

Let R be a commutative ring R with 1. In [PK Sharma, SM Bhatwadekar, A note on graphical
representation of rings, J. Algebra 176 (1995) 124–127], Sharma and Bhatwadekar defined …

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, Z (R) its set of zero-divisors, and Nil (R) its ideal of
nilpotent elements. The zero-divisor graph of R is Γ (R)= Z (R){0, with distinct vertices x and y …