# Coloring of commutative rings

```@article{Beck1988ColoringOC,
title={Coloring of commutative rings},
author={Istv{\'a}n Beck},
journal={Journal of Algebra},
year={1988},
volume={116},
pages={208-226}
}```
• I. Beck
• Published 1 July 1988
• Mathematics
• Journal of Algebra
924 Citations

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

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

### 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  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

• Mathematics
Communications 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

In 1988, Beck  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