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

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 )

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

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

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

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

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

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 [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

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
...