## 35 Citations

### On Zero-divisor Graphs Whose Cores Contain no Rectangles

- Mathematics
- 2011

This paper answers a question of Lu and Wu: How can one characterize the zero-divisor graphs which contain no rectangles? We prove that a graph which contains no rectangles is the zero-divisor graph…

### Minimal prime ideals and cycles in annihilating-ideal graphs

- Mathematics
- 2013

Let R be a commutative ring with identity and A(R) be the set of ideals with non-zero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)∗ = A(R)\{0}…

### SOME RESULTS ON THE INTERSECTION GRAPHS OF IDEALS OF RINGS

- Mathematics
- 2013

Let R be a ring with unity and I(R)* be the set of all nontrivial left ideals of R. The intersection graph of ideals of R, denoted by G(R), is a graph with the vertex set I(R)* and two distinct…

### Automorphisms of the zero-divisor graph of the ring of all n×n matrices over a finite field

- MathematicsDiscret. Math.
- 2016

### On realizing zero-divisor graphs of po-semirings

- Mathematics
- 2011

In this paper, we determine bipartite graphs and complete graphs with horns, which are realizable as zero-divisor graphs of po-semirings. As applications, we classify commutative rings $R$ whose…

### Some Results on Intersection Graphs of Ideals of Commutative Rings

- Mathematics
- 2020

The rings considered in this article are commutative with identity which admit at least one nonzero proper ideal. Let R be a ring. Recall that the intersection graph of ideals of R, denoted by G(R),…

### The Zero-Divisor Graph of a Commutative Semigroup: A Survey

- Mathematics
- 2017

Let S be a (multiplicative) commutative semigroup with 0. Associate to S a (simple) graph G(S) with vertices the nonzero zero-divisors of S, and two distinct vertices x and y are adjacent if and only…

### The Annihilating-Ideal Graph of a Commutative Ring with Respect to an Ideal

- Mathematics
- 2014

For a commutative ring R with identity, the annihilating-ideal graph of R, denoted 𝔸𝔾(R), is the graph whose vertices are the nonzero annihilating ideals of R with two distinct vertices joined by…

### On the coloring of the annihilating-ideal graph of a commutative ring

- MathematicsDiscret. Math.
- 2012

## References

SHOWING 1-10 OF 27 REFERENCES

### The Zero-Divisor Graphs Which Are Uniquely Determined By Neighborhoods

- Mathematics
- 2007

A nonempty simple connected graph G is called a uniquely determined graph, if distinct vertices of G have distinct neighborhoods. We prove that if R is a commutative ring, then Γ(R) is uniquely…

### The zero-divisor graph of a commutative semigroup

- Mathematics
- 2002

An undirected graph Γ(S) is associated to each commutative multiplicative semigroup S with 0. The vertices of the graph are labeled by the nonzero zero-divisors of S , and two vertices x,y are…

### A New Graph Structure of Commutative Semigroups

- Mathematics
- 2005

AbstractIn this paper, a new
zero-divisor graph $\overline{\G}(S)$ is defined and studied for a
commutative semigroup $S$ with zero element. The properties and
the structure of the graph are studied;…