Let R be a commutative ring with identity. The prime ideal sum graph of R, denoted by PIS
(R), is a graph whose vertices are nonzero proper ideals of R and two distinct vertices I and …

Let R be a ring (not necessarily commutative) with identity. The clean graph Cl (R) of a ring
R is a graph with vertices in form (e, u), where e is an idempotent and u is a unit of R; and …

The rings considered in this article are commutative with non-zero identity which are not
integral domains. Let R be a ring. Let Z (R) denote the set of all zero-divisors of R and we …

The annihilating-ideal graph of a commutative ring $ R $ with unity is defined as the graph
$\mathbb {AG}(R) $ with the vertex set is the set of all non-zero ideals with non-zero …

Let R be a commutative ring with identity which is not an integral domain. Let Z (R) denote
the set of all zero-divisors of R. Recall from [1] that the Armendariz graph of R denoted by A …

Let $ R $ be an associative ring and $ M $ be a monoid‌. ‌In this paper‌, ‌we introduce new kind
of graph structure asociated with zero-divisors of monoid ring $ R [M] $ ‌, ‌calling it the $ M …

In this paper, we study some basic properties of weakly zero-divisor graph of the ring Z p× Z
q× Z r, denoted by W Γ (Z p× Z q× Z r), where p, q and r are prime numbers greater than 2 …

Let $ R $ be a commutative ring with identity which is not an integral domain. Let $ Z (R) $
denote the set of all zero-divisors of $ R $. Recall from [1] that the Armendariz graph of $ R …

Let R be a ring (not necessarily commutative) with identity. The clean graph Cl (R) of a ring
R is a graph with vertices in form (e, u), where e is an idempotent and u is a unit of R; and …