In this book, we introduce several graphical representations of a ring. In the past three
decades, graphs constructed from algebraic structures have been studied extensively by …

Let R be a commutative ring with nonzero identity. We denote by AG (R) the annihilator
graph of R, whose vertex set consists of the set of nonzero zero-divisors of R, and two distint …

In this article the annihilating-ideal graph of the ring C (X) is studied. We have tried to
associate the graph properties of AG (X), the ring properties of C (X) and the topological …

In this paper we introduce and study the spectrum graph of a commutative ring R, denoted
by 𝔸𝔾s (R), that is, the graph whose vertices are all non-zero prime ideals of R with non …

Let $ S $ be a semigroup with $0 $ and $ R $ be a ring with $1 $. We extend the definition of
the zero-divisor graphs of commutative semigroups to not necessarily commutative …

The rings considered in this article are commutative with identity which are not integral
domains. Let R be a ring. An ideal I of R is said to be an annihilating ideal of R if there exists …

Let R be a commutative ring and A (R) be the set of all ideals with non-zero annihilators.
Assume that A∗(R)= A (R)⧹{(0)} and F (R) denote the set of all finitely generated ideals of R …

We have tried to translate some graph properties of AG (R) and Gamma (R) to the
topological properties of Zariski topology. We prove that Rad (Gamma (R)) and Rad (AG (R)) …

Let R be a commutative ring with identity and Nil (r) be the set of nilpotent elements of r. The
nil-graph of ideals of r is defined as the graph AGN (R) whose vertex set is {I:(0)≠ I⊲ RR and …

We translate some graph properties of AG (R) and Γ (R) to some topological properties of
Zariski topology. We prove that the facts “(1) The zero ideal of R is an anti fixed-place …