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 $1\neq 0$ and $ Z (R) $ its set of zero-divisors. The
zero-divisor graph of $ R $ is the (simple) graph $\Gamma (R) $ with vertices $ Z …

Let x∈ Zn and AI (x)={r∈ Zn: rx∈ I}. The annihilator ideal graph of Zn, denoted by AGI (Zn)
is the undirected graph with vertex set V (AGI (Zn))={x∈ Zn\I: xy∈ I, y∈ I}, and two distinct …

In this paper, R is a commutative ring with a non-zero identity and M is a unital R-module.
We introduce the comaximal colon ideal graph C*(R) and colon submodule graph C*(M); …

We explore generalizations and variations of the zero-divisor graph on commutative rings
with identity. A zero-divisor graph is a graph whose vertex set is the nonzero zero-divisors of …

Dari suatu ring komutatif R dengan elemen satuan dan ideal sejati I dari R dapat
didefinisikan graf annihilator ideal. Untuk suatu elemen x∈ R∖ I didefinisikan himpunan …

In this paper some properties of the complement of a new graph associated with a
commutative ring R are investigated. This new graph, denoted by W*(R), is an undirected …