## 924 Citations

### Clique number and Chromatic number of a graph associated to a Commutative Ring with Unity.

- Mathematics
- 2019

Let R be a commutative ring with unity (not necessarily finite). The ring R consider as a simple graph whose vertices are the elements of R with two distinct vertices x and y are adjacent if xy=0 in…

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

- MathematicsDiscret. Math.
- 2012

### The edge chromatic number of Γ I ( R )

- Mathematics
- 2018

For a commutative ring R and an ideal I of R, the ideal-based zero-divisor graph is the undirected graph ΓI(R) with vertices {x ∈ R−I : xy ∈ I for some y ∈ R−I}, where distinct vertices x and y are…

### Some non-chromatic rings

- Mathematics
- 1998

Let R be a commutative ring with identity. Consider R as a simple graph with vertices elements of R where any two distinct elements x, y ϵ R are adjacent if and only if xy = 0. Beck [2] conjectured…

### Some results on a spanning subgraph of the intersection graph of ideals of a commutative ring

- Mathematics
- 2015

The rings considered in this article are commutative with identity and which admit at least one nonzero proper ideal. For a ring R, we denote by I(R), the set of all proper ideals of R and let I(R)∗…

### Some results on the complement of a new graph associated to a commutative ring

- Mathematics
- 2017

The rings considered in this article are commutative with identity which are not fields. Let R be a ring. A. Alilou, J. Amjadi and Sheikholeslami introduced and investigated a graph whose vertex set…

### On a graph of ideals of a commutative ring

- MathematicsCommunications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
- 2019

In this paper, we introduce and investigate a new graph of a commutative ring R, denoted by G(R), with all nontrivial ideals of R as vertices, and two distinct vertices I and J are adjacent if and…

### Coloring of the annihilator graph of a commutative ring

- Mathematics
- 2016

Let R be a commutative ring with identity, and let Z(R) be the set of zero-divisors of R. The annihilator graph of R is defined as the graph AG(R) with the vertex set Z(R)∗ = Z(R)\{0}, and two…

### ZERO DIVISOR GRAPHS OF POSETS

- Mathematics
- 2014

In 1988, Beck [10] introduced the notion of coloring of a commutative ring R. Let G be a simple graph whose vertices are the elements of R and two vertices x and y are adjacent if xy = 0. The graph G…

### CO-MAXIMAL IDEAL GRAPHS OF COMMUTATIVE RINGS

- Mathematics
- 2012

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 $\mathscr{C}(R)$ to denote this graph, with its vertices the…

## References

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